# Algebraic Geometry 2000, Azumino (Advanced Studies in Pure Mathematics No. 36)

By: Shuki Saito (editor), Siegeru Mukai (editor), Luc Illusie (editor), Mark Green (editor), Sampei Usui (editor), Kazuya Kato (editor), E. J. N. Looijenga (editor)Hardback

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### Description

This conference proceedings volume contains survey and research articles on topics of current interest written by leading international experts. The topic of the symposium was 'Interactions of Algebraic Geometry, Hodge Theory, and Logarithmic Geometry from the Viewpoint of Degenerations'. The book contains four surveys on pencils of algebraic curves by T. Ashikaga and K. Konno; integral $p$-adic Hodge theory by C. Breuil; Hodge-Arakelov theory of elliptic curves by S. Mochizuki; and refined cycle maps by S. Saito.Also included are two results by Gabber on absolute purity theorem written by K. Fujiwara and research articles on the Picard-Lefschetz formula by L. Illusie, moduli spaces of rational elliptic surfaces by G. Heckman and E. Looijenga, moduli of curves of genus 4 by S. Kondo, and logarithmic Hodge theory by K. Kato, C. Nakayama, and S. Usui and its application to geometry by S. Saito. The volume is intended for researchers interested in algebraic geometry, particularly in the study of families of algebraic varieties and Hodge structures.

### Contents

Survey Articles: Global and local properties of pencils of algebraic curves by T. Ashikaga and K. Konno Integral $p$-adic Hodge theory by C. Breuil A survey of the Hodge-Arakelov theory of elliptic curves II by S. Mochizuki Refined cycle maps by M. Saito Research Articles: Independence of $\ell$ for intersection cohomology (after Gabber) by K. Fujiwara A proof of the absolute purity conjecture (after Gabber) by K. Fujiwara The moduli space of rational elliptic surfaces by G. Heckman and E. Looijenga Sur la formule de Picard-Lefschetz by L. Illusie Log $C^\infty$-functions and degenerations of Hodge structures by K. Kato, T. Matsubara, and C. Nakayama Borel-Serre spaces and spaces of $\mathrm{SL}(2)$-orbits by K. Kato and S. Usui The moduli space of curves of genus 4 and Deligne-Mostow's complex by S. Kondo Infinitesimal logarithmic Torelli problem for degenerating hypersurfaces in $\mathbb{P}^n$ by S. Saito Appendix by Atsuhi Ikeda.

### Product Details

• publication date: 15/10/2002
• ISBN13: 9784931469204
• Format: Hardback
• Number Of Pages: 442
• ID: 9784931469204
• weight: 822
• ISBN10: 4931469205

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