# Search Results for "degeneration-of-abelian-varieties-ergebnisse-der-mathematik-und-ihrer-grenzgebiete-3-folge-a-series-of-modern-surveys-in-mathematics"

## Degeneration of Abelian Varieties

**Author**: Gerd Faltings,Ching-Li Chai**Publisher:**Springer Science & Business Media**ISBN:**3662026325**Category:**Mathematics**Page:**318**View:**6231

A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.

## A Celebration of Algebraic Geometry

**Author**: Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil**Publisher:**American Mathematical Soc.**ISBN:**0821889834**Category:**Mathematics**Page:**599**View:**2160

This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

## Geometry, Analysis and Probability

*In Honor of Jean-Michel Bismut*

**Author**: Jean-Benoît Bost,Helmut Hofer,François Labourie,Yves Le Jan,Xiaonan Ma,Weiping Zhang**Publisher:**Birkhäuser**ISBN:**3319496387**Category:**Mathematics**Page:**361**View:**7950

This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.

## Cartesian Currents in the Calculus of Variations II

*Variational Integrals*

**Author**: Mariano Giaquinta,Both in the Department of Mathematics Mariano Giaquinta,Guiseppe Modica,Jiri Soucek**Publisher:**Springer Science & Business Media**ISBN:**9783540640103**Category:**Mathematics**Page:**700**View:**733

This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph

## Number Fields and Function Fields – Two Parallel Worlds

**Author**: Gerard van der Geer,B.J.J Moonen,René Schoof**Publisher:**Springer Science & Business Media**ISBN:**9780817643973**Category:**Mathematics**Page:**321**View:**5547

Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections

## Cartesian Currents in the Calculus of Variations I

*Cartesian Currents*

**Author**: Mariano Giaquinta,Giuseppe Modica,Jiri Soucek**Publisher:**Springer Science & Business Media**ISBN:**9783540640097**Category:**Mathematics**Page:**711**View:**5620

This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph