Joe Harris - Böcker

The primary goal of these lectures is to introduce a beginner to the finite-dimensional representations of Lie groups and Lie algebras. Intended to serve non-specialists, the concentration of the text is on examples. The general theory is developed sparingly, and then mainly as useful and unifying language to describe phenomena already encountered in concrete cases. The book begins with a brief tour through representation theory of finite groups, with emphasis determined by what is useful for Lie groups. The focus then turns to Lie groups and Lie algebras and finally to the heart of the course: working out the finite dimensional representations of the classical groups. The goal of the last portion of the book is to make a bridge between the example-oriented approach of the earlier parts and the general theory.

The primary goal of these lectures is to introduce a beginner to the finite­ dimensional representations of Lie groups and Lie algebras. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e.

This book is intended to introduce students to algebraic geometry; to give them a sense of the basic objects considered, the questions asked about them, and the sort of answers one can expect to obtain. It thus emplasizes the classical roots of the subject. For readers interested in simply seeing what the subject is about, this avoids the more technical details better treated with the most recent methods. For readers interested in pursuing the subject further, this book will provide a basis for understanding the developments of the last half century, which have put the subject on a radically new footing. Based on lectures given at Brown and Harvard Universities, this book retains the informal style of the lectures and stresses examples throughout; the theory is developed as needed. The first part is concerned with introducing basic varieties and constructions; it describes, for example, affine and projective varieties, regular and rational maps, and particular classes of varieties such as determinantal varieties and algebraic groups. The second part discusses attributes of varieties, including dimension, smoothness, tangent spaces and cones, degree, and parameter and moduli spaces.

The aim of this book is to provide a guide to a rich and fascinating subject: algebraic curves, and how they vary in families. The revolution that the field of algebraic geometry has undergone with the introduction of schemes, together with new ideas, techniques and viewpoints introduced by Mumford and others, have made it possible for us to understand the behavior of curves in ways that simply were not possible a half-century ago. This in turn has led, over the last few decades, to a burst of activity in the area, resolving longstanding problems and generating new and unforeseen results and questions. We hope to acquaint you both with these results and with the ideas that have made them possible. The book isn’t intended to be a definitive reference: the subject is developing too rapidly for that to be a feasible goal, even if we had the expertise necessary for the task. Our preference has been to focus on examples and applications rather than on foundations. When discussing techniqueswe’ve chosen to sacrifice proofs of some, even basic,results—particularly where we can provide a good reference— in order to show how the methods are used to study moduli of curves. Likewise, we often prove results in special cases which we feel bring out the important ideas with a minimum of technical complication.

The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his coworkers. It has allowed major progress in classical areas of algebraic geometry such as invariant theory and the moduli of curves. It integrates algebraic number theory with algebraic geometry, fulfilling the dreams of earlier generations of number theorists. This integration has led to proofs of some of the major conjectures in number theory (Deligne's proof of the Weil Conjectures, Faltings proof of the Mordell Conjecture). This book is intended to bridge the chasm between a first course in classical algebraic geometry and a technical treatise on schemes. It focuses on examples, and strives to show "what is going on" behind the definitions. There are many exercises to test and extend the reader's understanding. The prerequisites are modest: a little commutative algebra and an acquaintance with algebraic varieties, roughly at the level of a one-semester course. The book aims to show schemes in relation to other geometric ideas, such as the theory of manifolds. Some familiarity with these ideas is helpful, though not required.

The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his coworkers. It has allowed major progress in classical areas of algebraic geometry such as invariant theory and the moduli of curves. It integrates algebraic number theory with algebraic geometry, fulfilling the dreams of earlier generations of number theorists. This integration has led to proofs of some of the major conjectures in number theory (Deligne's proof of the Weil Conjectures, Faltings proof of the Mordell Conjecture). This book is intended to bridge the chasm between a first course in classical algebraic geometry and a technical treatise on schemes. It focuses on examples, and strives to show "what is going on" behind the definitions. There are many exercises to test and extend the reader's understanding. The prerequisites are modest: a little commutative algebra and an acquaintance with algebraic varieties, roughly at the level of a one-semester course. The book aims to show schemes in relation to other geometric ideas, such as the theory of manifolds. Some familiarity with these ideas is helpful, though not required.

This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.

This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.

In a world where we are constantly being asked to make decisions based on incomplete information, facility with basic probability is an essential skill. This book provides a solid foundation in basic probability theory designed for intellectually curious readers and those new to the subject. Through its conversational tone and careful pacing of mathematical development, the book balances a charming style with informative discussion. This text will immerse the reader in a mathematical view of the world, giving them a glimpse into what attracts mathematicians to the subject in the first place. Rather than simply writing out and memorizing formulas, the reader will come out with an understanding of what those formulas mean, and how and when to use them. Readers will also encounter settings where probabilistic reasoning does not apply or where intuition can be misleading. This book establishes simple principles of counting collections and sequences of alternatives, and elaborates on these techniques to solve real world problems both inside and outside the casino. Pair this book with the HarvardX online course for great videos and interactive learning: https://harvardx.link/fat-chance.

In a world where we are constantly being asked to make decisions based on incomplete information, facility with basic probability is an essential skill. This book provides a solid foundation in basic probability theory designed for intellectually curious readers and those new to the subject. Through its conversational tone and careful pacing of mathematical development, the book balances a charming style with informative discussion. This text will immerse the reader in a mathematical view of the world, giving them a glimpse into what attracts mathematicians to the subject in the first place. Rather than simply writing out and memorizing formulas, the reader will come out with an understanding of what those formulas mean, and how and when to use them. Readers will also encounter settings where probabilistic reasoning does not apply or where intuition can be misleading. This book establishes simple principles of counting collections and sequences of alternatives, and elaborates on these techniques to solve real world problems both inside and outside the casino. Pair this book with the HarvardX online course for great videos and interactive learning: https://harvardx.link/fat-chance.

This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988. It is intended to be, as the title suggests, a first introduction to the subject. Even so, a few words are in order about the purposes of the book. Algebraic geometry has developed tremendously over the last century. During the 19th century, the subject was practiced on a relatively concrete, down-to-earth level; the main objects of study were projective varieties, and the techniques for the most part were grounded in geometric constructions. This approach flourished during the middle of the century and reached its culmination in the work of the Italian school around the end of the 19th and the beginning of the 20th centuries. Ultimately, the subject was pushed beyond the limits of its foundations: by the end of its period the Italian school had progressed to the point where the language and techniques of the subject could no longer serve to express or carry out the ideas of its best practitioners.

This textbook provides readers with a working knowledge of the modern theory of complex projective algebraic curves. Also known as compact Riemann surfaces, such curves shaped the development of algebraic geometry itself, making this theory essential background for anyone working in or using this discipline. Examples underpin the presentation throughout, illustrating techniques that range across classical geometric theory, modern commutative algebra, and moduli theory. The book begins with two chapters covering basic ideas, including maps to projective space, invertible sheaves, and the Riemann-Roch theorem. Subsequent chapters alternate between a detailed study of curves up to genus six and more advanced topics such as Jacobians, Hilbert schemes, moduli spaces of curves, Severi varieties, dualizing sheaves, and linkage of curves in 3-space. Three chapters treat the refinements of the Brill-Noether theorem, including applications and a complete proof of the basic result. Two chapters on free resolutions, rational normal scrolls, and canonical curves build context for Green's conjecture. The book culminates in a study of Hilbert schemes of curves through examples. A historical appendix by Jeremy Gray captures the early development of the theory of algebraic curves. Exercises, illustrations, and open problems accompany the text throughout. The Practice of Algebraic Curves offers a masterclass in theory that has become essential in areas ranging from algebraic geometry itself to mathematical physics and other applications. Suitable for students and researchers alike, the text bridges the gap from a first course in algebraic geometry to advanced literature and active research.

The Crimson Chronicles, that foul bible of blood, foretells thecoming of Chaos, the Destroyer, and his servants on earth. Since her earliestdays, Vampirella has stood between that vicious cult and their Mad God's plans.But when an ancient prophecy of doom is uncovered and a new push to resurrectthe foulest demons from the pit is revealed, it's clear Vampirella won't be ableto take them on alone. Enter The Scarlet Legion — assembled to keep thedark things at bay and protect this world from the evils which lie beyond. Theonly question is, will they see Vampirella as friend... or foe?Collecting the 5-issue mini-series in one volume, with bonus material and acomplete cover gallery.

Spinning out of Alan Moore's retelling of the ageless horror classic,Dracula has come to America to play out his timeless narrative in this brave,New World. Only he didn't realize ANOTHER vampire already beat him to it. Drawnto one another across continents and centuries by a mysterious force, bothVampirella and Bram Stoker's immortal monster find themselves sucked into atime-tossed epic of love, hate, death, and damnation. But can an epic built forone vampire possibly hold them both?Collecting the six-issue series in one volume, along with a complete covergallery featuring art by Joe Linsner.

Rock n' roll legend Alice Cooper has never been a stranger to the mystic andthe macabre. His stage shows were the stuff of legend, featuring snakes andpyrotechnics, the invocation of dark themes and darker forces. But while he wasa legend in the waking world, few knew his service as "The Lord of Nightmares"beyond it, where he watched over us while we dreamed, and delivered horrors untothe deserving. Only someone took it all away from him, cast him out of hisrealm, and locked him away. No longer enslaved to the Clan Black, Alice Cooperwill reclaim his dark throne at all costs. All hail the Godfather of ShockRock!Collects the complete Alice Cooper comic book series issues#1-6.

Over a year has passed since industrialist adventurer Chas Worthingtonfounded the New Texas Settlement upon a floating continent of trash. But whilegrowth has been strong, true sovereignty and statehood will come at a cost evenhe cannot afford. The frontier tale of sci-fi, scoundrels, mayhem, and monsterscontinues!

When fugitive oil heir Chas Worthington settles the infamous Great PacificGarbage Patch and declares it his own sovereign nation, the reality of theenvironmental catastrophe is only the beginning of his odyssey. Chas takes NewTexas from wilderness to a fledgling country in a frontier tale of sci-fi,scoundrels, mayhem, and monsters.In this third volume, a hunter of both weapons and men comes to New Texasseeking both. Chas Worthington will have to choose between what’s right,what’s wrong, and just what the real cost of doing business is if he wantsto lead his nation out of a crisis and avert all-out civil war.

Phenomenon, conspiracy, or delusion? “Kelvin” Melvin Reyes was only three years old when Spontaneous Human Combustion took his father from him. He’s since devoted his life to exploring the mystery behind the phenomenon, searching for a pattern and predictors that he might save others from that same fiery fate. But the closer he gets to his goal, the further things lead down a well of secrets, horrors, and terrible truths. Is SHC real? And if so, can it be stopped?What follows is a supernatural trip down a suburban rabbit hole as Melvin’s quest to honor his father’s memory unlocks the mysteries of his town’s dark past and his own family secrets. From acclaimed writer and filmmaker Joe Harris (Ghost Projekt, The X-Files) comes a slow-burn horror thriller of obsession, belief, and restitution.

As the Cold War widened in the 1950s, military hero George Kutter and his family trained to be legacy survivors in the event of an atomic exchange with the Soviet Union. Prepared to wait out the aftermath of nuclear war, they were subjected to myriad simulations, scenarios and stresses in hopes of helping salvage something of their family, their country and humanity from the ashes of a conflict with the Russians that never happened. But when a group of hunting buddies stumble upon an old fallout shelter buried in the present-day Pennsylvania wilderness and end up locked inside, they quickly learn that “truth” is just a matter of conditioning, while a crash course in paranoia, propaganda and control awaits.What was the nature of the secret Archonite initiative? What lengths did the United States go to in order to prepare for all-out war and its aftermath? What did the Kutter Family endure in perpetration for their duty? And if World War III never broke out… why are they still down there?

Phenomenon, conspiracy, or delusion? "Kelvin" Melvin Reyes was only threeyears old when Spontaneous Human Combustion took his father from him. He's sincedevoted his life to exploring the mystery behind the phenomenon, searching for apattern and predictors that he might save others from that same fiery fate. Butthe closer he gets to his goal, the further things lead down a well of secrets,horrors, and terrible truths. Is SHC real? And, if so, can it bestopped?