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.

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Information

Publisher

Academic Press

Year

2014

ISBN

9781483265056

Topic

Mathematics

Subtopic

Abstract Algebra

Index

Mathematics

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