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.

Readership

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

Table of Contents

• T. Ashikaga and K. Konno -- Global and local properties of pencils of algebraic curves
• C. Breuil -- Integral \(p\)-adic Hodge theory
• S. Mochizuki -- A survey of the Hodge-Arakelov theory of elliptic curves II
• M. Saito -- Refined cycle maps

• K. Fujiwara -- Independence of \(\ell\) for intersection cohomology (after Gabber)
• K. Fujiwara -- A proof of the absolute purity conjecture (after Gabber)
• G. Heckman and E. Looijenga -- The moduli space of rational elliptic surfaces
• L. Illusie -- Sur la formule de Picard-Lefschetz
• K. Kato, T. Matsubara, and C. Nakayama -- Log \(C^\infty\)-functions and degenerations of Hodge structures
• K. Kato and S. Usui -- Borel-Serre spaces and spaces of \(\mathrm{SL}(2)\)-orbits
• S. Kondo -- The moduli space of curves of genus 4 and Deligne-Mostow's complex
• S. Saito -- Infinitesimal logarithmic Torelli problem for degenerating hypersurfaces in \(\mathbb{P}^n\)
• Appendix by Atsuhi Ikeda