Proceedings of the symposium on algebraic geometry in East Asia / editors, Akira Ohbuchi ... [et al.].

Format:

Book

Conference/Event

Contributor:

Ohbuchi, Akira.

Conference Name:

Symposium on Algebraic Geometry in East Asia (2001 : Kyoto, Japan)

Symposium on Algebraic Geometry in East Asia.

Language:

English

Subjects (All):

Geometry, Algebraic--Congresses.

Geometry--Congresses.

Physical Description:

1 online resource (273 p.)

Other Title:

Algebraic geometry in East Asia

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2002.

Language Note:

English

Summary:

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.

Contents:

Preface; Contents; Introduction to Arakelov Geometry Shu Kawaguchi, Atsushi Moriwaki and Kazuhiko Yamaki; Introduction; 1. Arithmetic Chow Group; 1.1. Introduction; 1.2. Currents; 1.3. Arithmetic Variety and Arithmetic Chow Group; 1.4. Arithmetic Intersection Theory; 1.5. Arithmetic Chow Group and Push-forward of Arithmetic Cycles; 1.6. Height of Arithmetic Variety; 2. Arithmetic Riemann-Roch Theorem; 2.1. Characteristic Forms; 2.2. The Bott-Chern Secondary Characteristic Class; 2.3. Arithmetic characteristic class; 2.4. Analytic torsion and Quillen metric

2.5. Arithmetic Riemann-Roch Theorem 3. Existence of a Small Section; 3.1. Small Section; 3.2. Arithmetic Euler Characteristic; 3.3. Arithmetic Hilbert-Samuel Theorem and the Existence of a Small Section; 3.4. The comparison of Lp-norm and sup-norm; 3.5. Proof of Theorem 3.3.3; 3.6. Proof of the arithmetic Hilbert-Samuel theorem; 4. Adelic metric and admissible metric; 4.1. Adelic metric and intersection number; 4.2. Admissible metric and cubic metric; 5. Arithmetic height function; 5.1. Definition of arithmetic height functions and their properties; 5.2. Height functions on abelian varieties

5.3. Adelic metric and height function5.4. Intersection number of nef C -hermitian line bundles; 5.5. Relation of height function and intersection number; 6. Bogomolov's conjecture; 6.1. Equidistribution theorem; 6.2. The proof of Bogomolov's conjecture; 7. A generalization of conjectures of Bogomolov and Lang; 7.1. Statement of Bogomolov plus Lang; 7.2. Small points with respect to a group of finite rank; 7.3. Proof of Bogomolov plus Lang; Appendix; references; Double Covering of Smooth Algebraic Curves Changho Keem; 0 Introduction.; 1 Existence of base-point-free pencils of degree g - 1.

2 Irreducibility of Wi-l(C) for a bi-elliptic curve.3 Existence of base-point-free pencils of degree g - 2.; 4 Double covering of a general curve of higher genus.; 5 Irreducibility of W (C) for double coverings.; 6 Epilogue; an odd end with general k-gonal curves.; REFERENCES; Algebraic Surfaces with Quotient Singularities - Including Some Discussion on Automorphisms and Fundamental Groups JongHae Keum and De-Qi Zhang; INTRODUCTION; TERMINOLOGY AND NOTATION; SECTION 1. PRELIMINARIES; SECTION 2. NORMAL ALGEBRAIC SURFACES Y WITH KODAIRA DIMENSION (Yo) = AND FANO VARIETIES

SECTION 3. NORMAL ALGEBRAIC SURFACES Y WITH KODAIRA DIMENSION (Yo) = o'SECTION 4. NORMAL ALGEBRAIC SURFACES Y WITH KODAIRA DIMENSION (Yo) = 1,2; SECTION 5. AUTOMORPHISMS OF ALGEBRAIC SURFACES - SMOOTH SURFACE CASE; SECTION 6. AUTOMORPHISMS OF ALGEBRAIC SURFACES - SINGULAR SURFACE CASE; ACKNOWLEDGEMENT; REFERENCES; Linear Series of Irregular Varieties Jungkai A . Chen and Christopher D. Hacon; 1. INTRODUCTION; 2. FOURIER-MUKAI TRANSFORMS; 3. ADJOINT LINEAR SERIES OF IRREGULAR VARIETIES; 4. NON-VANISHING OF ADJOINT LINEAR SERIES; 5. PLURICANONICAL; REFERENCES

Hecke Curves on the Moduli Space of Vector Bundles Jun-Muk Hwang

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611908607

9781281908605

1281908606

9789812705105

9812705104