Algebraic Geometry and Commutative Algebra : In Honor of Masayoshi Nagata.

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 -- 1. Introduction -- First Chapter. YOUNG TABLEAUX AND DETERMINANTAL POLYNOMIALS IN BINOMIAL COEFFICIENTS -- 2. Tableaux and monomials -- 3. Determinantal polynomials of any width -- 4. Determinantal polynomials of width two -- Second Chapter. ENUMERATION OF YOUNG TABLEAUX -- 5. Counting tableaux of any width -- 6. Bitableaux -- 7. Counting bitableaux -- 8. Counting monomials -- 9. Bitableaux and monomials -- Third Chapter. UNIVERSAL DETERMINANTAL IDENTITY -- 10. Preamble -- 11. The mixed size case -- 12. The cardinality condition -- 13. The maximal size case -- 14. The basic case -- 15. Laplace development -- 16. The full depth case -- 17. Deduction of the full depth case -- 18. The straightening law -- 19. Problem -- Fourth Chapter. APPLICATIONS TO IDEAL THEORY -- 20. Determinantal loci -- 21. Vector spaces and homogeneous rings -- 22. Standard basis -- 23. Second fundamental theorem of invariant theory -- 24. Generalized second fundamental theorem of invariant theory -- References -- A Conjecture of Sharp -The Case of Local Rings with dim non CM ≤ 1 or dim ≤ 5 -- 1. Introduction -- 2. Sharp's Conjecture -- 3. Proofs of Theorem 1.1 and Theorem 1.2 -- References -- A Structure Theorem for Power Series Rings -- 1. We suppose that there is given a commutative diagram -- 2. We may replace B by C = R[X,Y]/(f1,...„fm) -- 3. -- 4. Proof of the Theorem -- 5. Corollary -- References -- On Rational Plane Sextics with Six Tritangents Wolf BARTH* and Ross MOORE -- 0. Introduction -- 1. Some Polynomials -- 2. The sextic space curve S -- 3. The projected curves Sx -- 4. The double plane X -- 5. The double plane Y -- 6. Moduli.

7. Explanations -- References -- On Rings of Invariants of Finite Linear Groups -- 1. Fundamental groups -- 2. Proof of Theorem A -- 3. Additional results -- References -- Invariant Differentials -- 1. Introduction -- 2. Use of the étale slice theorem -- 3. The ñnite group case -- References -- Classification of Polarized Manifoldsof Sectional Genus Two -- Introduction -- Notation, Convention and Terminology -- 1. Classification, first step -- 2. The case K ~ (3 - n)L -- 3. The case of a hyperquadric fíbration over a curve -- 4. Polarized surfaces of sectional genus two -- Appendix -- References -- Affine Surfaces with κ ≤ 1 -- Introduction -- 1. Surfaces with K = -∞ -- 2. The case K{S) = 0 -- 3. The case K{S) = 1 -- 4. Examples K{S) = 2 -- References -- On the Convolution Algebra of Distributionson Totally Disconnected Locally Compact Groups -- 0. Introduction -- 1. Finite w-distribution -- 2. Action of homeomorphisms and multiplication by functions -- 3. Generators of S(X, w -- V) -- 4. Action of Τ on vector valued functions -- 5. Tensor product of distributions -- 6. Convolution -- 7. Representation of G -- 8. Regular representation -- 9. Projection operator -- 10. D-modules and S.-modules -- 11. D-modules and ε-modules -- 12. Proof of Theorem 1 -- 13. Proof of Theorem 2 -- References -- The Local Cohomology Groups of an Affine Semigroup Ring -- Introduction -- 1. Affine semigroup rings and the associated cones -- 2. Complexes associated to an affine semigroup ring -- 3. The dualizing complex and the local cohomology groups -- 4. Serre's condition (S2) -- References -- Quaternion Extensions -- Definitions, Notations and Some Necessary Facts -- Introduction. -- I. Quaternion extensions and quadratic forms -- II. Fields that admit quaternion extensions -- III. Automatic realizations -- IV. Polynomials with Galois group Qs -- Acknowledgement.

References -- On the Discriminants of the Intersection Form on Néron-Severi Groups -- 0. Introduction -- 1. Preliminaries -- 2. Bilinear forms -- 3. The Discriminant of the intersection form -- 4. Examples -- 5. A K3 surface -- References -- On Complete Ideals in Regular Local Rings -- Introduction -- 1. Point bases and completions of ideals in regular local rings -- 2. Simple complete ideals corresponding to infinitely near points -- 3. The length of a complete ideal (dimension 2) -- 4. Unique factorization for complete ideals (dimension 2) -- References -- On a Compactification of a Moduli Space of Stable Vector Bundles on a Rational Surface -- Introduction. -- 1. Some remarks on semi-stable sheaves -- 2. Semi-stable sheaves on a rational surface -- 3. Semi-stability of the universal extension -- 4. Image of ф ( Γ, C1 , C2) -- 5. Image of ф(r,0,C2) -- 6. Good polarizations and the case of rank 2 -- References -- On the Dimension of Formal Fibres of a Local Ring -- Introduction. -- 1. Formal fibres -- 2. Some cases where α{A) is smaller than dim A - 1 -- References -- On the Classification Problem of Embedded Lines in Characteristic ρ -- 1. Introduction -- 2. Expansions and Their Calculus -- 3. The Defining Equations -- 4. αi = 0 -- 5. Other Coiijectiires -- References -- A Cancellation Theorem for Projective Modules over Finitely Generated Rings -- 1. Introduction -- 2. Cancellation -- 3. Projective stable ranges -- References -- Semi-ampleness of the Numerically Effective Part of Zariski Decomposition II -- 0. Introduction -- 1. Preliminary -- 2. Zariski decomposition -- 3. Canonical rings -- References -- On the Moduli of Todorov Surfaces -- 1. Equidistant binary linear codes -- 2. K3 surfaces with ordinary double points -- 3 . Double covers of surfaces with ordinary double points -- 4. Involutions on canonical surfaces -- 5. Todorov surfaces.

6. Embeddings of Todorov lattices -- 7. The moduli of Todorov surfaces -- 8. Concluding remarks -- Appendix -- References -- Curves, K3 Surfaces and Fano 3-folds of Genus ≤ 10 -- 1. Preliminary -- 2. Proof of Theorem 0.2 in the case g = 10 -- 3. Generic K3 surfaces of genus 7,8, and 9 -- 4. Generic K3 surface of genus 6 -- 5. Fano 3-folds of genus 10 -- 6. Curves of genus ≤ 9 -- References -- Threefolds Homeomorphic toa Hyperquadric in P4 -- 0. Introduction -- 1. Hyperquadrics in P4 -- 2. Lemmas -- 3. A complete intersection L = DnD -- 4. Proof of (3.2) -- 5. Proof of (3.3) -- 6. Proof of (3.4) -- 7. Proof of (3.5) -- 8. Proof of (3.6) -- 9. Proof of (0.1) -- Appendix -- References.

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