Fabrizio Catanese – författare

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19 produkter

Del 4 - SISSA Springer Series
Algebraic Curves and Surfaces
A History of Shapes
AvLaurent Busé,Fabrizio Catanesem. fl.
Inbunden, Engelska, 2023
1 456 kr
Skickas inom 10-15 vardagar
This volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces and the classification theorem of algebraic surfaces by Castelnuovo and Enriques; the use of such a classical geometric approach, as the one introduced by Castelnuovo, to study linear systems of hypersurfaces; and the algebraic methods used to find implicit equations of parametrized algebraic curves and surfaces, ranging from classical elimination theory to more modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Since our subject has a long and venerable history, this book cannot cover all the details of this broad topic, theory and applications, but it is meant to serve as a guide for both young mathematicians to approach the subject from a classical and yet computational perspective, and for experienced researchers as a valuable source for recent applications.
Algebraic Curves and Surfaces
A History of Shapes
AvElisa Postinghel,Fabrizio Catanesem. fl.
E-bok
Engelska, 2023
1 435 kr
Läs direkt efter köp
This volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces and the classification theorem of algebraic surfaces by Castelnuovo and Enriques; the use of such a classical geometric approach, as the one introduced by Castelnuovo, to study linear systems of hypersurfaces; and the algebraic methods used to find implicit equations of parametrized algebraic curves and surfaces, ranging from classical elimination theory to more modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Since our subject has a long and venerable history, this book cannot cover all the details of this broad topic, theory and applications, but it is meant to serve as a guide for both young mathematicians to approach the subject from a classical and yet computational perspective, and for experienced researchers as a valuable source for recent applications.
Algebraic Curves and Surfaces : A History of Shapes
AvLaurent Busé,Fabrizio Catanese
Engelska, 2023
646 kr
Skickas inom 5-8 vardagar
Del 4 - SISSA Springer Series
Algebraic Curves and Surfaces
A History of Shapes
AvLaurent Busé,Fabrizio Catanesem. fl.
Häftad, Engelska, 2024
1 122 kr
Skickas inom 10-15 vardagar
This volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces and the classification theorem of algebraic surfaces by Castelnuovo and Enriques; the use of such a classical geometric approach, as the one introduced by Castelnuovo, to study linear systems of hypersurfaces; and the algebraic methods used to find implicit equations of parametrized algebraic curves and surfaces, ranging from classical elimination theory to more modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Since our subject has a long and venerable history, this book cannot cover all the details of this broad topic, theory and applications, but it is meant to serve as a guide for both young mathematicians to approach the subject from a classical and yet computational perspective, and for experienced researchers as a valuable source for recent applications.
Del 31 - Lecture Notes of the Unione Matematica Italiana
Varieties of Nodal Surfaces, Coding Theory and Discriminants of Cubic Hypersurfaces
AvFabrizio Catanese
Häftad, Engelska, 2026
1 210 kr
Skickas inom 5-8 vardagar
This research book deals with some classical problems of algebraic geometry, notably the problem about the maximal number of singularities that a nodal variety can have, and the problem about the description of the components of the Severi varieties of nodal surfaces. A complete solution is found for nodal quartic surfaces in 3-space and for nodal K3 surfaces. New striking results are found also for quintic and sextic surfaces. The main focus of the book is the relation of nodal surfaces with binary coding theory, introduced by Beauville: two codes are attached to a nodal projective surface, which are invariants of these components, and in some cases determine them.The book contains a very concrete introduction to binary coding theory and new applications of Nikulin's theory of primitive embeddings of lattices. The book contains also a thorough investigation of cubic hypersurfaces and their singularities, and the associated discriminant surfaces, providing new constructions for surfaces of degree 5 and 6 with the maximal number of nodes. A surprising relation is found between the Barth 65 nodal surface and the Doro-Hall graph. The book is addressed to algebraic geometers and experts of coding theory. It is also meant to be a source of many beautiful classical constructions, due to Kummer, Togliatti and others, which should be of interest to graduate students who want to get to know classical projective geometry.
Varieties of Nodal Surfaces, Coding Theory and Discriminants of Cubic Hypersurfaces
AvFabrizio Catanese
E-bok
Engelska, 2026
1 587 kr
Läs direkt efter köp
This research book deals with some classical problems of algebraic geometry, notably the problem about the maximal number of singularities that a nodal variety can have, and the problem about the description of the components of the Severi varieties of nodal surfaces. A complete solution is found for nodal quartic surfaces in 3-space and for nodal K3 surfaces. New striking results are found also for quintic and sextic surfaces. The main focus of the book is the relation of nodal surfaces with binary coding theory, introduced by Beauville: two codes are attached to a nodal projective surface, which are invariants of these components, and in some cases determine them.The book contains a very concrete introduction to binary coding theory and new applications of Nikulin's theory of primitive embeddings of lattices. The book contains also a thorough investigation of cubic hypersurfaces and their singularities, and the associated discriminant surfaces, providing new constructions for surfaces of degree 5 and 6 with the maximal number of nodes. A surprising relation is found between the Barth 65 nodal surface and the Doro-Hall graph. The book is addressed to algebraic geometers and experts of coding theory. It is also meant to be a source of many beautiful classical constructions, due to Kummer, Togliatti and others, which should be of interest to graduate students who want to get to know classical projective geometry.
Algebraic Geometry
A Volume in Memory of Paolo Francia
AvMauro C. Beltrametti,Fabrizio Catanesem. fl.
Inbunden, Engelska, 2002
3 044 kr
Skickas inom 5-8 vardagar
The volume consists of invited refereed research papers. The contributions cover a wide spectrum in algebraic geometry, from motives theory to numerical algebraic geometry and are mainly focused on higher dimensional varieties and Minimal Model Program and surfaces of general type.A part of the articles grew out a Conference in memory of Paolo Francia (1951-2000) held in Genova in September 2001 with about 70 participants.
Algebraic Geometry
A Volume in Memory of Paolo Francia
AvClaudio Pedrini,Antonio Lanterim. fl.
E-bok
PDF, Engelska, 2008
3 021 kr
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The volume consists of invited refereed research papers. The contributions cover a wide spectrum in algebraic geometry, from motives theory to numerical algebraic geometry and are mainly focused on higher dimensional varieties and Minimal Model Program and surfaces of general type. A part of the articles grew out a Conference in memory of Paolo Francia (1951-2000) held in Genova in September 2001 with about 70 participants.
Del 15 - Lecture Notes of the Unione Matematica Italiana
Homological Mirror Symmetry and Tropical Geometry
AvRicardo Castano-Bernard,Fabrizio Catanesem. fl.
Häftad, Engelska, 2014
1 233 kr
Skickas inom 10-15 vardagar
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as “degenerations” of the corresponding algebro-geometric objects.
Homological Mirror Symmetry and Tropical Geometry
AvIlia Zharkov,Yan Soibelmanm. fl.
E-bok
PDF, Engelska, 2014
1 587 kr
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The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as “degenerations” of the corresponding algebro-geometric objects.
Global Aspects of Complex Geometry
AvFabrizio Catanese,Hélène Esnaultm. fl.
Inbunden, Engelska, 2006
1 122 kr
Skickas inom 10-15 vardagar
This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry
Global Aspects of Complex Geometry
AvThomas Peternell,Klaus Hulekm. fl.
E-bok
PDF, Engelska, 2006
1 427 kr
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This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kähler geometry, and group actions to Hodge theory and characteristic p-geometry.
Written by established experts this book will be a must for mathematicians working in Complex Geometry
Classification of Irregular Varieties
Minimal Models and Abelian Varieties. Proceedings of a Conference held in Trento, Italy, 17-21 December, 1990
AvCiro Ciliberto,Fabrizio Catanesem. fl.
E-bok
PDF, Engelska, 2006
363 kr
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Transcendental Methods in Algebraic Geometry
Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), held in Cetraro, Italy, July 4-12, 1994
AvAndrej N. Tyurin,Gang Tianm. fl.
E-bok
PDF, Engelska, 2006
718 kr
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Del 1515 - Lecture Notes in Mathematics
Classification of Irregular Varieties
Minimal Models and Abelian Varieties. Proceedings of a Conference held in Trento, Italy, 17-21 December, 1990
AvEdoardo Ballico,Fabrizio Catanesem. fl.
Häftad, Engelska, 1992
285 kr
Skickas inom 10-15 vardagar
M. Andreatta,E.Ballico,J.Wisniewski: Projective manifolds containing large linear subspaces; - F.Bardelli: Algebraic cohomology classes on some specialthreefolds; - Ch.Birkenhake,H.Lange: Norm-endomorphisms of abelian subvarieties; - C.Ciliberto,G.van der Geer: On the jacobian of ahyperplane section of a surface; - C.Ciliberto,H.Harris,M.Teixidor i Bigas: On the endomorphisms of Jac (W1d(C)) when p=1 and C has general moduli; - B. van Geemen: Projective models of Picard modular varieties; - J.Kollar,Y.Miyaoka,S.Mori: Rational curves on Fano varieties; - R. Salvati Manni: Modular forms of the fourth degree; A. Vistoli: Equivariant Grothendieck groups and equivariant Chow groups; - Trento examples; Open problems
Del 1646 - Lecture Notes in Mathematics
Transcendental Methods in Algebraic Geometry
Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), held in Cetraro, Italy, July 4-12, 1994
AvJean-Pierre Demailly,Thomas Peternellm. fl.
Häftad, Engelska, 1996
564 kr
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Presents lectures given at the 3rd session of the Centro Internazionale Matematico Estivo, held in Cetraro, Italy, in July 1994. The topics covered include four manifolds, line bundles and manifolds of semi-positive curvature.
Del 1938 - Lecture Notes in Mathematics
Symplectic 4-Manifolds and Algebraic Surfaces
Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003
AvDenis Auroux,Fabrizio Catanesem. fl.
Häftad, Engelska, 2008
564 kr
Skickas inom 10-15 vardagar
Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics.The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.
Symplectic 4-Manifolds and Algebraic Surfaces
Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003
AvGang Tian,Ivan Smithm. fl.
E-bok
PDF, Engelska, 2008
718 kr
Läs direkt efter köp
Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics.
The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.
Global Aspects of Complex Geometry
AvFabrizio Catanese,Hélène Esnaultm. fl.
Häftad, Engelska, 2010
1 122 kr
Skickas inom 10-15 vardagar
This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry

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Fabrizio Catanese – författare

Algebraic Curves and Surfaces

Algebraic Curves and Surfaces

Algebraic Curves and Surfaces : A History of Shapes

Algebraic Curves and Surfaces

Varieties of Nodal Surfaces, Coding Theory and Discriminants of Cubic Hypersurfaces

Varieties of Nodal Surfaces, Coding Theory and Discriminants of Cubic Hypersurfaces

Algebraic Geometry

Algebraic Geometry

Homological Mirror Symmetry and Tropical Geometry

Homological Mirror Symmetry and Tropical Geometry

Global Aspects of Complex Geometry

Global Aspects of Complex Geometry

Classification of Irregular Varieties

Transcendental Methods in Algebraic Geometry

Classification of Irregular Varieties

Transcendental Methods in Algebraic Geometry

Symplectic 4-Manifolds and Algebraic Surfaces

Symplectic 4-Manifolds and Algebraic Surfaces

Global Aspects of Complex Geometry

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