# Algebraic Geometry 2000, Azumino

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*Sampei Usui; Mark Green; Luc Illusie; Kazuya Kato; Eduard Looijenga; Siegeru Mukai; Shuji Saito*

A publication of the Mathematical Society of Japan

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 1) pencils of algebraic curves by T.
Ashikaga and K. Konno; 2) integral \(p\)-adic Hodge theory by C. Breuil;
3) Hodge-Arakelov theory of elliptic curves by S. Mochizuki; and 4) 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.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.

Volumes in this series are freely available electronically 5 years post-publication.

#### Readership

Graduate students and research mathematicians interested in algebra and algebraic geometry.