Hyperbolicity Of Projective Hypersurfaces

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Hyperbolicity Of Projective Hypersurfaces

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Author : Simone Diverio
language : en
Publisher: Springer
Release Date : 2016-07-12

Hyperbolicity Of Projective Hypersurfaces written by Simone Diverio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-12 with Mathematics categories.

This book presents recent advances on Kobayashi hyperbolicity in complex geometry, especially in connection with projective hypersurfaces. This is a very active field, not least because of the fascinating relations with complex algebraic and arithmetic geometry. Foundational works of Serge Lang and Paul A. Vojta, among others, resulted in precise conjectures regarding the interplay of these research fields (e.g. existence of Zariski dense entire curves should correspond to the (potential) density of rational points). Perhaps one of the conjectures which generated most activity in Kobayashi hyperbolicity theory is the one formed by Kobayashi himself in 1970 which predicts that a very general projective hypersurface of degree large enough does not contain any (non-constant) entire curves. Since the seminal work of Green and Griffiths in 1979, later refined by J.-P. Demailly, J. Noguchi, Y.-T. Siu and others, it became clear that a possible general strategy to attack this problem was to look at particular algebraic differential equations (jet differentials) that every entire curve must satisfy. This has led to some several spectacular results. Describing the state of the art around this conjecture is the main goal of this work.

Panoramas Et Synth Ses

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Author : B. Claudon
language : en
Publisher:
Release Date : 2022

Panoramas Et Synth Ses written by B. Claudon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

A Survey On Hiperbolicity Of Projective Hypersurfaces

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Author : Simone Diverio
language : en
Publisher:
Release Date : 2011

A Survey On Hiperbolicity Of Projective Hypersurfaces written by Simone Diverio and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Geometry, Hyperbolic categories.

Weighted Projective Hypersurfaces

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Author : Daniel Nelson Dore
language : en
Publisher:
Release Date : 2016

Weighted Projective Hypersurfaces written by Daniel Nelson Dore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.

Real Hypersurfaces In Hermitian Symmetric Spaces

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Author : Jürgen Berndt
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-03-21

Real Hypersurfaces In Hermitian Symmetric Spaces written by Jürgen Berndt and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-21 with Mathematics categories.

Hermitian symmetric spaces are an important class of manifolds that can be studied with methods from Kähler geometry and Lie theory. This work gives an introduction to Hermitian symmetric spaces and their submanifolds, and presents classifi cation results for real hypersurfaces in these spaces, focusing on results obtained by Jürgen Berndt and Young Jin Suh in the last 20 years.

Versality Properties Of Projective Hypersurfaces

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Author : A. A. Du Plessis
language : en
Publisher:
Release Date : 1998

Versality Properties Of Projective Hypersurfaces written by A. A. Du Plessis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Weighted Projective Hypersurfaces With Extreme Invariants

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Author : Louis Esser
language : en
Publisher:
Release Date : 2023

Weighted Projective Hypersurfaces With Extreme Invariants written by Louis Esser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

The goal of this dissertation is to study weighted projective hypersurfaces and their application to optimization problems in algebraic geometry. First, we generalize and strengthen several well-known results on the automorphisms of hypersurfaces due to Grothendieck-Lefschetz and Matsumura-Monsky to the weighted setting. Then, we construct special examples of weighted projective hypersurfaces with extreme properties. These are used to prove strong asymptotics on certain invariants from birational geometry as dimension increases. In particular, we show that the minimum volume of smooth varieties of general type approaches zero doubly exponentially with dimension; we also show that the index of mildly singular Calabi-Yau varieties can grow doubly exponentially with dimension. For several classes of varieties, we conjecture the optimal bounds on volume or index in every dimension; these conjectures are supported by low-dimensional evidence.

Some Isoparametric Hypersurfaces Of A Complex Hyperbolic Space And Their Counterparts In Anti De Sitter Space Time

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Author : Michael H. Vernon
language : en
Publisher:
Release Date : 1985

Some Isoparametric Hypersurfaces Of A Complex Hyperbolic Space And Their Counterparts In Anti De Sitter Space Time written by Michael H. Vernon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Hypersurfaces categories.

Algebraic Hyperbolicity Of Very General Hypersurfaces And Their Complements

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Author : Wern Yeen Yeong
language : en
Publisher:
Release Date : 2023

Algebraic Hyperbolicity Of Very General Hypersurfaces And Their Complements written by Wern Yeen Yeong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

A Metric On Moduli Spaces Of Projective Hypersurfaces

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Author : Carl Anton Haverl
language : en
Publisher:
Release Date : 1996

A Metric On Moduli Spaces Of Projective Hypersurfaces written by Carl Anton Haverl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Hypersurfaces categories.