Algebraic Geometry and Commutative Algebra

In Honor of Masayoshi Nagata

Hiroaki Hijikata, Heisuke Hironaka, Masaki Maruyama

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780123480323
• eBook ISBN: 9781483265056
• Topic: Mathematics
• Subtopic: Abstract Algebra
• Index: Mathematics

Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata presents a collection of papers on algebraic geometry and commutative algebra in honor of Masayoshi Nagata for his significant contributions to commutative algebra. Topics covered range from Weierstrass models and endomorphism algebras of abelian varieties to the generic Torelli theorem for hypersurfaces in compact irreducible hermitian symmetric spaces. Coarse moduli spaces for curves are also discussed, along with discriminants of curves of genus 2 and arithmetic surfaces. Comprised of 14 chapters, this volume begins by describing a basic fibration as a Weierstrass model, with emphasis on elliptic threefolds with a section. The reader is then introduced to canonical bundles of analytic surfaces of class VII0 with curves; Lifting Problem on ideal-adically complete noetherian rings; and the canonical ring of a curve. Subsequent chapters deal with algebraic surfaces for regular systems of weights; elementary transformations of algebraic vector bundles; the irreducibility of the first differential equation of Painlevé; and F-pure normal rings of dimension two. The book concludes with an assessment of the existence of some curves. This monograph will be a useful resource for practitioners and researchers in algebra and geometry.

Table of contents

• Front Cover
• Algebraic Geometry and Commutative Algebra: In Honor of Masayoshi NAGATA
• Copyright Page
• Table of Contents
• Table of Contents of Volume I
• Chapter 1. On Weierstrass Models
• Chapter 2. Canonical Bundles of Analytic Surfaces of Class VII
• Chapter 3. Ideal-adic Completion of Noetherian Rings II
• Chapter 4. Endomorphism Algebras of Abelian Varieties
• Chapter 5. On the Canonical Ring of a Curve
• Chapter 6. Algebraic Surfaces for Regular Systems of Weights
• Chapter 7. Generic Torelli Theorem for Hypersurfaces in Compact Irreducible Hermitian Symmetric Spaces
• Chapter 8. A Variety Which Contains a P1-fiber Space as an Ample Divisor
• Chapter 9. How Coarse the Coarse Moduli Spaces for Curves Are!
• Chapter 10. Elementary Transformations of Algebraic Vector Bundles II
• Chapter 11. Discriminants of Curves of Genus 2 and Arithmetic Surfaces
• Chapter 12. On the Irreducibility of the First Differential Equation of Painlevé
• Chapter 13. Study of F-purity in Demension Two
• Chapter 14. A Note on the Existence of Some Curves