A Metric On Moduli Spaces Of Projective Hypersurfaces

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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.

Compact Moduli Of Surfaces In Three Dimensional Projective Space

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Author : Kristin DeVleming
language : en
Publisher:
Release Date : 2018

Compact Moduli Of Surfaces In Three Dimensional Projective Space written by Kristin DeVleming and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.

The main goal of this paper is to construct a compactification of the moduli space of degree d[greater than or equal to]5 hypersurfaces in P3, i.e. a parameter space whose interior points correspond to (equivalence classes of) smooth hypersurfaces in P3 and whose boundary points correspond to degenerations of such hypersurfaces. Following a trail blazed by numerous others (see, for example, work of Koll\'ar, Shepherd-Barron, Alexeev, and Hacking), we consider a hypersurface D in P3 as a pair (P3, D) satisfying certain properties. We find a modular compactification of such pairs and use their properties to classify the pairs on the boundary to the moduli space.

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.

Quasi Projective Moduli For Polarized Manifolds

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

Quasi Projective Moduli For Polarized Manifolds written by Eckart Viehweg 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.

The concept of moduli goes back to B. Riemann, who shows in [68] that the isomorphism class of a Riemann surface of genus 9 ~ 2 depends on 3g - 3 parameters, which he proposes to name "moduli". A precise formulation of global moduli problems in algebraic geometry, the definition of moduli schemes or of algebraic moduli spaces for curves and for certain higher dimensional manifolds have only been given recently (A. Grothendieck, D. Mumford, see [59]), as well as solutions in some cases. It is the aim of this monograph to present methods which allow over a field of characteristic zero to construct certain moduli schemes together with an ample sheaf. Our main source of inspiration is D. Mumford's "Geometric In variant Theory". We will recall the necessary tools from his book [59] and prove the "Hilbert-Mumford Criterion" and some modified version for the stability of points under group actions. As in [78], a careful study of positivity proper ties of direct image sheaves allows to use this criterion to construct moduli as quasi-projective schemes for canonically polarized manifolds and for polarized manifolds with a semi-ample canonical sheaf.

The Moduli Space Of Curves

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Author : Robert H. Dijkgraaf
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Moduli Space Of Curves written by Robert H. Dijkgraaf 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.

The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.

Moduli Spaces

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Author : Leticia Brambila
language : en
Publisher: Cambridge University Press
Release Date : 2014-03-13

Moduli Spaces written by Leticia Brambila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-13 with Mathematics categories.

A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

K Hler Metric And Moduli Spaces

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Author : T. Ochiai
language : en
Publisher: Academic Press
Release Date : 2013-10-22

K Hler Metric And Moduli Spaces written by T. Ochiai and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Mathematics categories.

Kähler Metric and Moduli Spaces, Volume 18-II covers survey notes from the expository lectures given during the seminars in the academic year of 1987 for graduate students and mature mathematicians who were not experts on the topics considered during the sessions about partial differential equations. The book discusses basic facts on Einstein metrics in complex geometry; Einstein-Kähler metrics with positive or non-positive Ricci curvature; Yang-Mills connections; and Einstein-Hermitian metrics. The text then describes the tangent sheaves of minimal varieties; Ricci-Flat Kähler metrics on affine algebraic manifolds; and degenerations of Kähler-Einstein. The moduli of Einstein metrics on a K3 surface and degeneration of Type I and the uniformization of complex surfaces are also considered. Mathematicians and graduate students taking differential and analytic geometry will find the book useful.

The Moduli Space Of Hypersurfaces Whose Singular Locus Has High Dimension

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Author : Kaloyan Stefanov Slavov
language : en
Publisher:
Release Date : 2011

The Moduli Space Of Hypersurfaces Whose Singular Locus Has High Dimension written by Kaloyan Stefanov Slavov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

Fix integers n and b with n =/> 3 and 1 =/

The Geometry Of Moduli Spaces Of Sheaves

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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-27

The Geometry Of Moduli Spaces Of Sheaves written by Daniel Huybrechts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-27 with Mathematics categories.

This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Moduli Of Curves

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Author : Joe Harris
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06

Moduli Of Curves written by Joe Harris 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 2006-04-06 with Mathematics categories.

A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results and open problems about important topics which are not covered in detail.