José Luis Cisneros Molina – författare

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject.This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject.This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects.

Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects.

Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects.

This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more.Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research.This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex.Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research.This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex.Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

The singularities are the zeros of the form. Open books, which naturally appear in singularity theory as foliations with singular set the binding. These important examples highlight the deep connections between foliations and singularity theory.

This is the fifth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. Singularities are ubiquitous in mathematics and science in general, and singularity theory is a crucible where different types of mathematical problems converge, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects.This Volume V focuses on singular holomorphic foliations, which is a multidisciplinary field and a whole area of mathematics in itself. Singular foliations arise, for instance, by considering:The fibers of a smooth map between differentiable manifolds, with singularities at the critical points.The integral lines of a vector field, or the action of a Lie group on a manifold. The singularities are the orbits with special isotropy.The kernel of appropriate 1-forms. The singularities are the zeros of the form.Open books, which naturally appear in singularity theory as foliations with singular set the binding.These important examples highlight the deep connections between foliations and singularity theory. This volume, like its companion Volume VI, also focused on foliations, consists of nine chapters, authored by world experts, which provide in-depth and reader-friendly introductions to some of the foundational aspects of the theory. These introductions also give insights into important lines of further research. The volume starts with a foreword by one of the current world leaders in the theory of complex foliations.The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

The singularities are the zeroes of the form.Open books, which naturally appear in singularity theory, are foliations with singular set the binding. These important examples highlight the deep connections between foliations and singularity theory.

This is the sixth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. Singularities are ubiquitous in mathematics and science in general, and singularity theory is a crucible where different types of mathematical problems converge, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects.This Volume VI goes together with Volume V and focuses on singular holomorphic foliations, which is a multidisciplinary field and a whole area of mathematics in itself. Singular foliations arise, for instance, by considering:The fibers of a smooth map between differentiable manifolds, with singularities at the critical points.The integral lines of a vector field, or the action of a Lie group on a manifold. The singularities are the orbits with special isotropy.The kernel of appropriate 1-forms. The singularities are the zeroes of the form.Open books, which naturally appear in singularity theory, are foliations with singular set the binding.These important examples highlight the deep connections between foliations and singularity theory. This volume consists of nine chapters, authored by world experts, which provide in-depth and reader-friendly introductions to some of the foundational aspects of the theory. These introductions also give insights into important lines of further research. Volume VI ends with an Epilogue by one of the current world leaders in the theory of complex foliations, with plenty of open questions and ideas for further research.The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Then, we look at the perturbation theory of polynomials and linear operators, complex analytic frontal singularities, the global singularity theory of differentiable maps, and the singularities of holomorphic functions from a global point of view.

This is the eight volume of the Handbook of Geometry and Topology of Singularities, a series that provides an accessible account of the state of the art of the subject, its frontiers and its interactions with other areas of research. This volume consists of twelve chapters with reader-friendly introductions to several important topics and aspects of singularity theory, such as: Plane curve singularities studied by means of divides, which capture a lot of their topology. Viro’s method to study the topology of real algebraic varieties, providing a wide range of  possible combinations of topological and combinatorial invariants.Local tropicalization, a technique for attaching a combinatorial object to germs of subvarieties of algebraic tori and toric varieties. The theory of Zariski pairs and superisolated singularities.The McKay correspondence, a deep connection that links group theory, algebraic geometry, and representation theory.Calculations with Characteristic Cycles, a deep concept in the interplay between algebraic geometry, representation theory and microlocal analysis. The monodromy zeta functions in singularity theory. The singularities of the minimal model program of complex quasi-projective varieties. A general theory of Thom polynomials associated to the classification of map-germs.A discussion on indices and residues, intertwining the theories of complex analytic singular varieties and singular holomorphic foliations.The Monodromy in Integral Geometry and PDE.The topological theory of Hyperplane Arrangements.The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings.Singularity theory is at the crossroad of various branches of mathematics and science in general.