[PDF] Compactifying Moduli Spaces eBook

Author : Paul Hacking
Publisher : Birkhäuser
Page : 141 pages
File Size : 29,26 MB
Release : 2016-02-04
Category : Mathematics
ISBN : 3034809212

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This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps. Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.

Author : Martin C. Olsson
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 26,65 MB
Release : 2008-08-25
Category : Mathematics
ISBN : 354070518X

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This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.

Author : Francesco Scattone
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 13,81 MB
Release : 1987
Category : Mathematics
ISBN : 0821824376

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This paper is concerned with the problem of describing compact moduli spaces for algebraic [italic]K3 surfaces of given degree 2[italic]k.

Author : Valery Alexeev
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 47,16 MB
Release : 2012
Category : Mathematics
ISBN : 0821868993

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This book contains the proceedings of the conference on Compact Moduli and Vector Bundles, held from October 21-24, 2010, at the University of Georgia. This book is a mix of survey papers and original research articles on two related subjects: Compact Moduli spaces of algebraic varieties, including of higher-dimensional stable varieties and pairs, and Vector Bundles on such compact moduli spaces, including the conformal block bundles. These bundles originated in the 1970s in physics; the celebrated Verlinde formula computes their ranks. Among the surveys are those that examine compact moduli spaces of surfaces of general type and others that concern the GIT constructions of log canonical models of moduli of stable curves. The original research articles include, among others, papers on a formula for the Chern classes of conformal classes of conformal block bundles on the moduli spaces of stable curves, on Looijenga's conjectures, on algebraic and tropical Brill-Noether theory, on Green's conjecture, on rigid curves on moduli of curves, and on Steiner surfaces.

Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 345 pages
File Size : 16,31 MB
Release : 2010-05-27
Category : Mathematics
ISBN : 1139485822

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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.

Author : Valery Alexeev
Publisher : Birkhäuser
Page : 112 pages
File Size : 20,50 MB
Release : 2015-05-18
Category : Mathematics
ISBN : 3034809158

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This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete examples are developed that take advantage of the intricate interplay between Algebraic Geometry and Combinatorics. Compactifications of moduli spaces play a crucial role in Number Theory, String Theory, and Quantum Field Theory – to mention just a few. In particular, the notion of compactification of moduli spaces has been crucial for solving various open problems and long-standing conjectures. Further, the book reports on compactification techniques for moduli spaces in a large class where computations are possible, namely that of weighted stable hyperplane arrangements (shas).

Author : Ching-Li Chai
Publisher : Cambridge University Press
Page : 348 pages
File Size : 39,64 MB
Release : 1985-12-12
Category : Mathematics
ISBN : 9780521312530

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The main result of this monograph is to prove the existence of the toroidal compactification over Z(1/2).