Examples Of Hypersurfaces With Rational Singularities

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Examples Of Hypersurfaces With Rational Singularities

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Author : Robert Rowen Curtis
language : en
Publisher:
Release Date : 1993

Examples Of Hypersurfaces With Rational Singularities written by Robert Rowen Curtis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

Singularities And Topology Of Hypersurfaces

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Author : Alexandru Dimca
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Singularities And Topology Of Hypersurfaces written by Alexandru Dimca and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Le Cycles And Hypersurface Singularities

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Author : David Massey
language : en
Publisher: Springer
Release Date : 2006-11-14

Le Cycles And Hypersurface Singularities written by David Massey and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

This book describes and gives applications of an important new tool in the study of complex analytic hypersurface singularities: the Lê cycles of the hypersurface. The Lê cycles and their multiplicities - the Lê numbers - provide effectively calculable data which generalizes the Milnor number of an isolated singularity to the case of singularities of arbitrary dimension. The Lê numbers control many topological and geometric properties of such non-isolated hypersurface singularities. This book is intended for graduate students and researchers interested in complex analytic singularities.

Birational Geometry Of Hypersurfaces

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Author : Andreas Hochenegger
language : en
Publisher: Springer Nature
Release Date : 2019-10-08

Birational Geometry Of Hypersurfaces written by Andreas Hochenegger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-08 with Mathematics categories.

Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results. The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side. Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.

Complex Hypersurface Singularities With Application In Complex Geometry Algebraic Geometry And Lie Algebra

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Author : Stephen Shing-Toung Yau
language : en
Publisher:
Release Date : 1993

Complex Hypersurface Singularities With Application In Complex Geometry Algebraic Geometry And Lie Algebra written by Stephen Shing-Toung Yau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Hypersurfaces categories.

Singularities And Complexity In Cr Geometry

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Author : Jiri Lebl
language : en
Publisher:
Release Date : 2007

Singularities And Complexity In Cr Geometry written by Jiri Lebl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.

Several related questions in CR geometry are studied. First, the structure of the singular set of Levi-flat hypersurfaces is investigated. The singularity is completely characterized when it is a submanifold of codimension 1, and partial information is gained about higher codimension cases.

Hypersurface Sections And Obstructions

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Author : Kurt Behnke
language : de
Publisher:
Release Date : 1989

Hypersurface Sections And Obstructions written by Kurt Behnke and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.

Normal Surface Singularities

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Author : András Némethi
language : en
Publisher: Springer Nature
Release Date : 2022-10-07

Normal Surface Singularities written by András Némethi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-07 with Mathematics categories.

This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of the theory of normal surface singularities. This includes a comprehensive presentation of the properties of the link (as an oriented 3-manifold) and of the invariants associated with a resolution, combined with the structure and special properties of the line bundles defined on a resolution. A recurring theme is the comparison of analytic and topological invariants. For example, the Poincaré series of the divisorial filtration is compared to a topological zeta function associated with the resolution graph, and the sheaf cohomologies of the line bundles are compared to the Seiberg–Witten invariants of the link. Equivariant Ehrhart theory is introduced to establish surgery-additivity formulae of these invariants, as well as for the regularization procedures of multivariable series. In addition to recent research, the book also provides expositions of more classical subjects such as the classification of plane and cuspidal curves, Milnor fibrations and smoothing invariants, the local divisor class group, and the Hilbert–Samuel function. It contains a large number of examples of key families of germs: rational, elliptic, weighted homogeneous, superisolated and splice-quotient. It provides concrete computations of the topological invariants of their links (Casson(–Walker) and Seiberg–Witten invariants, Turaev torsion) and of the analytic invariants (geometric genus, Hilbert function of the divisorial filtration, and the analytic semigroup associated with the resolution). The book culminates in a discussion of the topological and analytic lattice cohomologies (as categorifications of the Seiberg–Witten invariant and of the geometric genus respectively) and of the graded roots. Several open problems and conjectures are also formulated. Normal Surface Singularities provides researchers in algebraic and differential geometry, singularity theory, complex analysis, and low-dimensional topology with an invaluable reference on this rich topic, offering a unified presentation of the major results and approaches.

Hypersurfaces With Many Singularities

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Author :
language : en
Publisher:
Release Date : 2005

Hypersurfaces With Many Singularities written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

Part 1: Known Constructions. The present work starts with a large survey of the classical subject of hypersurfaces with many singularities. The maximum number mu^n(d) of singularities on a hypersurface of degree d in P^n(C) is known in very few cases only, e.g. in P^3(C) for d=6. Apart from such exceptions, there only exist upper and lower bounds. Part 2: New Constructions. For low degree d, it is often possible to obtain better results than those given by the general bounds. In this work, we present some algorithmic approaches for these cases, one of which uses computer algebra in characteristic 0. The other algorithmic methods are based on a search over finite fields. Lifting the experimentally found hypersurfaces using their geometry or arithmetic yields e.g. a surface of degree 7 with 99 real ordinary double points and a surface of degree 9 with 226 ordinary double points. These constructions give the first lower bounds for mu^3(d) for odd degree d5 which exceed the general bound. Moreover, our algorithm has the potential of being applied to many other concrete problems in algebraic geometry. Besides these algorithmic approaches, we describe a construction of hypersurfaces of degree d in P^n with many A_j-singularities, j>=2. The proof of their existence is based on the theory of dessins d'enfants. These constructions exceed the known lower bounds in most cases and yield in particular new asymptotic lower bounds for all j>=2, n>=3. Part 3: Visualization. We close this work with an application of our new visualization software surfex which combines the strengths of several existing programs: We describe how to construct nice affine equations for all 45 topological types of real cubic surfaces.

Le Cycles And Hypersurface Singularities

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Author : David Massey
language : en
Publisher:
Release Date : 2014-09-01

Le Cycles And Hypersurface Singularities written by David Massey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.