Algebraic Geometry and Commutative Algebra

In Honor of Masayoshi Nagata

Hiroaki Hijikata, Heisuke Hironaka, Masaki Maruyama

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780123480316
• eBook ISBN:
  9781483265186
• Topic: Mathematics
• Subtopic: Geometry
• 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 power series rings and rings of invariants of finite linear groups to the convolution algebra of distributions on totally disconnected locally compact groups. The discussion begins with a description of several formulas for enumerating certain types of objects, which may be tabular arrangements of integers called Young tableaux or some types of monomials. The next chapter explains how to establish these enumerative formulas, with emphasis on the role played by transformations of determinantal polynomials and recurrence relations satisfied by them. The book then turns to several applications of the enumerative formulas and universal identity, including including enumerative proofs of the straightening law of Doubilet-Rota-Stein and computations of Hilbert functions of polynomial ideals of certain determinantal loci. Invariant differentials and quaternion extensions are also examined, along with the moduli of Todorov surfaces and the classification problem of embedded lines in characteristic p. 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
• Foreword
• Table of Contents of Volume II
• Determinantal Loci and Enumerative Combinatorics of Young Tableaux
• A Conjecture of Sharp —The Case of Local Rings with dim non CM ≤ 1 or dim ≤ 5
• A Structure Theorem for Power Series Rings
• On Rational Plane Sextics with Six Tritangents Wolf BARTH* and Ross MOORE
• On Rings of Invariants of Finite Linear Groups
• Invariant Differentials
• Classification of Polarized Manifoldsof Sectional Genus Two
• Affine Surfaces with κ ≤ 1
• On the Convolution Algebra of Distributionson Totally Disconnected Locally Compact Groups
• The Local Cohomology Groups of an Affine Semigroup Ring
• Quaternion Extensions
• On the Discriminants of the Intersection Form on Néron-Severi Groups
• On Complete Ideals in Regular Local Rings
• On a Compactification of a Moduli Space of Stable Vector Bundles on a Rational Surface
• On the Dimension of Formal Fibres of a Local Ring
• On the Classification Problem of Embedded Lines in Characteristic ρ
• A Cancellation Theorem for Projective Modules over Finitely Generated Rings
• Semi-ampleness of the Numerically Effective Part of Zariski Decomposition II
• On the Moduli of Todorov Surfaces
• Curves, K3 Surfaces and Fano 3-folds of Genus ≤ 10
• Threefolds Homeomorphic toa Hyperquadric in P4