Local and global methods in algebraic geometry : conference in honor of Lawrence Ein's 60th birthday, May 12-15, 2016, University of Illinois at Chicago, Chicago, Illinois / Nero Budur [and three others], editors.

Format:

Book

Contributor:

Budur, Nero, 1977- editor.

Ein, Lawrence, honoree.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 712

Contemporary mathematics, 712 0271-4132

Language:

English

Subjects (All):

Ein, Lawrence.

Geometry, Algebraic--Congresses.

Geometry, Algebraic.

Festschriften.

Physical Description:

1 online resource (370 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2018]

Summary:

This volume contains the proceedings of the conference Local and Global Methods in Algebraic Geometry, held from May 12-15, 2016, at the University of Illinois at Chicago, in honor of Lawrence Ein's 60th birthday. The articles cover a broad range of topics in algebraic geometry and related fields, including birational geometry and moduli theory, analytic and positive characteristic methods, geometry of surfaces, singularity theory, hyper-Kähler geometry, rational points, and rational curves.

Contents:

Cover

Title page

Contents

Preface

Scientific program

Some remarks on the work of Lawrence Ein

References

Contractible curves on a rational surface

1. Introduction

2. Preliminaries

3. The contraction theorem

4. Basics of the theory of peeling

5. The peeling approach to the contraction theorem

On the canonical map of some surfaces isogenous to a product

1. Introduction and state of the art on canonical surfaces of high degree in \PP³,\PP⁴,\PP⁵

2. Representations yielding an affine, respectively a projective embedding, of a finite group

3. Canonical maps of Galois coverings and of surfaces isogenous to a product

4. Surfaces with record winning high canonical degree

5. New double canonical surfaces

Degeneration of differentials and moduli of nodal curves on 3 surfaces

2. Semistable degenerations and the abstract log complex

3. The 3 case

4. Proof of Proposition 3.4

Weak Brill-Noether for rational surfaces

3. Strong exceptional collections and resolutions

4. Blowups of \P² revisited

5. Del Pezzo surfaces

Excellence in prime characteristic

2. Excellence

3. Maps inverse to Frobenius

4. Examples of non-excellent rings

Motivic zeta functions and infinite cyclic covers

2. Infinite cyclic cover of finite type

3. Motivic infinite cyclic zeta functions

4. Relation with the Denef-Loeser motivic zeta function

5. Further specializations of the motivic infinite cyclic zeta function

6. Motivic zeta functions for arbitrary divisors. Relation to the monodromy conjecture

Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun

A. Introduction.

B. Proof of the main statement

C. Generic vanishing

D. Singular metrics on pushforwards of adjoint line bundles

E. Pushforwards of relative pluricanonical bundles

A strongly geometric general residual intersection

2. General residual intersections

3. Invariants of singularities under a general residual intersection

Quadratic solutions of quadratic forms

1. Surfaces containing many circles

2. Maps of \p¹ to quadrics

3. Rational curves on quadrics

4. Degenerate maps of \p²

5. Veronese surfaces in quadric 4-folds

6. Quadratic maps up to coordinate changes

7. Quadrics of dimension ≥5

8. Orthogonal Grassmannians

9. Symmetric squares of orthogonal Grassmannians

Non-Cohen-Macaulay canonical singularities

2. Non-\CM singularities via failure of Kodaira vanishing

3. The construction of Lauritzen and Rao

4. A Fano variety violating Kodaira vanishing

Full cones swept out by minimal rational curves on irreducible Hermitian symmetric spaces as examples of varieties underlying geometric substructures

1. Introduction and motivation

2. Background materials and results

3. Sub-VMRTs structures modeled on full cones of minimal rational curves in the Hermitian symmetric case

4. Algebraicity of germs of sub-VMRT structures modeled on certain full cones of minimal rational curves

5. Intrinsically flat sub-VMRT structures modeled on certain full cones of minimal rational curves

6. Examples of non-standard sub-VMRT structures modeled on full cones of rational curves

7. Concluding Remarks

A boundedness conjecture for minimal log discrepancies on a fixed germ

2. Minimal log discrepancies: definition and basic facts.

3. Generic limits: bounding the order of the ideal of the point

4. A proof of the conjecture in dimension 2

5. A proof of the conjecture in the monomial case

6. Connection with ACC

7. Three equivalent conjectures

The Wahl map of one-nodal curves on K3 surfaces

Introduction

1. Generalities on Gaussian maps

2. The surjectivity of ⁰( )

3. The gaussian map on

Skoda's ideal generation from vanishing theorem for semipositive Nakano curvature and Cauchy-Schwarz inequality for tensors

1. Algebraic Formulation and Application of Skoda's Ideal Generation

2. Cauchy-Schwarz Inequality for Tensors

3. Nakano Curvature of Bundle and Twisting by Metric of Trivial Line Bundle

4. Vanishing Theorem and Solution of ∂ Equation for Nonnegative Nakano Curvature

5. Proof of Skoda's Result on Ideal Generation

6. Variants of Skoda's Ideal Generation

7. Comparison with Original Proof of Skoda's Ideal Generation

Hyper-Kähler compactification of the intermediate Jacobian fibration of a cubic fourfold: The twisted case

2. Deforming and constructing hyper-Kähler manifolds

3. The twisted intermediate Jacobian fibration: smooth and 1-nodal case

4. Descent

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-4850-5