Commutative Algebra Expository Papers Dedicated To David Eisenbud On The Occasion Of His 65th Birthday Irena Peeva Ed by Irena Peeva (ed.) 9781461452928, 1461452929 instant download after payment.

This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper unders. Read more... Commutative Algebra; Preface; Contents; Lazarsfeld-Mukai Bundles and Applications; 1 Definition, Properties, the First Applications; 1.1 Definition and First Properties; 1.2 Simple and Non-simple Lazarsfeld-Mukai Bundles; 1.3 The Petri Conjecture Without Degenerations; 1.4 Mukai Manifolds of Picard Number One; 2 Constancy of Invariants of K3-Sections; 2.1 Constancy of the Gonality. I; 2.2 Constancy of the Clifford Index; 2.3 Constancy of the Gonality. II; 2.4 Parameter Spaces of Lazarsfeld-Mukai Bundles and Dimension of Brill-Noether Loci; 3 Green's Conjecture for Curves on K3 Surfaces. 3.1 Koszul Cohomology3.2 Statement of Green's Conjecture; 3.3 Voisin's Approach; 3.4 The Role of Lazarsfeld-Mukai Bundles in the Generic Green Conjecture and Consequences; 3.5 Green's Conjecture for Curves on K3 Surfaces; 4 Counterexamples to Mercat's Conjecture in Rank Two; References; Some Applications of Commutative Algebra to String Theory; 1 Introduction; 2 Categorical Topological Field Theory; 2.1 Closed String Theories; 2.2 Open-Closed Strings; 2.3 Topological Conformal Field Theory; 2.4 Hochschild Cohomology; 3 Toric Geometry and Phases; 3.1 Tilting Collections. 3.2 Complete Intersections3.3 Landau-Ginzburg Theories; 3.4 Hochschild Cohomology; 4 Monodromy; 4.1 K-Theory; 4.2 The GKZ System; 4.3 A Calabi-Yau and Landau-Ginzburg Example; 4.4 Monodromy of the Structure Sheaf; References; Measuring Singularities with Frobenius: The Basics; 1 Introduction; 2 Characteristic Zero: Log Canonical Threshold and Multiplier Ideals; 2.1 Analytic Approach; 2.2 Computing Complex Singularity Exponent by Monomializing; 2.3 Algebro-Geometric Approach; 2.4 The Canonical Divisor of a Map; 2.5 Computations of Log Canonical Thresholds. 2.6 Multiplier Ideals and Jumping Numbers3 Positive Characteristic: The Frobenius Map and F-Thresholds; 3.1 The Frobenius Map; 3.2 F-Threshold; 3.3 Comparison of F-Threshold and Multiplicity; 3.4 Computing F-Thresholds; 3.5 Comparison of F-Thresholds and Log Canonical Thresholds; 3.6 Test Ideals and F-Thresholds; 3.7 An Interpretation of F-Thresholds and Test Ideals Using Differential Operators; 4 Unifying the Prime Characteristic and Zero Characteristic Approaches; 4.1 Idea of Reduction Modulo p; 4.2 Trace; References; Three Flavors of Extremal Betti Tables; 1 Introduction; 2 Preliminaries. 3 Extremal Betti Tables in the Graded Case4 Extremal Betti Tables in the Local Case; 5 Extremal Betti Tables in the Multigraded Case; References; p-1-Linear Maps in Algebra and Geometry; 1 Introduction; 2 Preliminaries on Frobenius; 2.1 Prerequisites and Notation; 2.2 Frobenius and Pushforward; 2.3 Frobenius Pullback and the Projection Formula; 2.4 Exercises; 3 p-e-Linear Maps: Definition and Examples; 3.1 The Cartier Isomorphism; 3.2 Grothendieck Trace of Frobenius; 3.3 The Trace Map for Singular Varieties; 3.4 Exercises; 4 Connections with Divisors; 4.1 A Generalization with Line Bundles