Algebraic geometry in East Asia : proceedings of the symposium on algebraic geometry in East Asia [which was held in International Institute for Advanced Studies (IIAS), Kyoto, Japan, during August 3 to August10, 2001

This book presents a unified approach on nonparametric estimators for models of independent observations, jump processes and continuous processes. New estimators are defined and their limiting behavior is studied. From a practical point of view, the book expounds on the construction of estimators for functionals of processes and densities, and provides asymptotic expansions and optimality properties from smooth estimators. It also presents new regular estimators for functionals of processes, compares histogram and kernel estimators, compares several new estimators for single-index models, and it examines the weak convergence of the estimators Introduction to Arakelov Geometry (S Kawaguchi et al.); Double Covering of Smooth Algebraic Curves (C Keem); Algebraic Surfaces with Quotient Singularities - Including Some Discussion on Automorphisms and Fundamental Groups (J Keum & D-Q Zhang); Linear Series of Irregular Varieties (J A Chen & C D Hacon); Hecke Curves on the Moduli Space of Vector Bundles (J-M Hwang); Minimal Resolution via Grobner Basis (Y Ito); Deformation Theory of Smoothable Semi Log Canonical Surfaces (Y Lee); Modular Curves and Some Related Issues (V NguyenKhac); On the Asymptotic Behavior of Admissible Variations of Mixed Hodge Structure (G Pearlstein); Degeneration of SL(n)-Bundles on a Reducible Curve (X-T Sun); Refined Brill-Noether Locus and Non-Abelian Zeta Functions for Elliptic Curves (L Weng) This book is the proceedings of the conference “Algebraic Geometry in East Asia” which was held in International Institute for Advanced Studies (IIAS) during August 3 to August 10, 2001.As the breadth of the topics covered in this proceedings demonstrate, the conference was indeed successful in assembling a wide spectrum of East Asian mathematicians, and gave them a welcome chance to discuss current state of algebraic geometry. This volume constitutes the proceedings of a symposium on algebraic geometry, held in Kyoto, Japan, in August 2001. Topics covered include: Arakelov geometry; degeneration of SL(n)-bundles on a reducible curve; linear series of irregular varieties; and minimal resolution via Grobner basis.