Algebraic Geometry and Commutative Algebra

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.

Contenu

Determinantal Loci and Enumerative Combinatorics of Young Tableaux

A Conjecture of Sharp - The Case of Local Rings with dim nonCM = 1 or dim = 5

A Structure Theorem for Power Series Rings

On Rational Plane Sextics with Six Tritangents

On Rings of Invariants of Finite Linear Groups

Invariant Differentials

Classification of Polarized Manifolds of Sectional Genus Two

Affine Surfaces with K = 1

On the Convolution Algebra of Distributions on 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 p

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 to a Hyperquadric in P4

On Weierstrass Models

Canonical Bundles of Analytic Surfaces of Class VII0

Ideal-Adic Completion of Noetherian Rings II

Endomorphism Algebras of Abelian Varieties

On the Canonical Ring of a Curve

Algebraic Surfaces for Regular Systems of Weights (with an Appendix by Isao Naruki)

Generic Torelli Theorem for Hypersurfaces in Compact Irreducible Hermitian Symmetric Spaces

A Variety Which Contains a P1-Fiber Space as an Ample Divisor

How Coarse the Coarse Moduli Spaces for Curves Are?

Elementary Transformations of Algebraic Vector Bundles II

Discriminants of Curves of Genus 2 and Arithmetic Surfaces

On the Irreducibility of the Fürst Differential Equation of Painlevé

Study of F-purity in Dimension Two

A Note on the Existence of Some Curves