**Contemporary Mathematics**

Volume: 712;
2018;
355 pp;
Softcover

MSC: Primary 13; 14; 32; 53;

**Print ISBN: 978-1-4704-3488-5
Product Code: CONM/712**

List Price: $117.00

AMS Member Price: $93.60

MAA Member Price: $105.30

**Electronic ISBN: 978-1-4704-4850-9
Product Code: CONM/712.E**

List Price: $117.00

AMS Member Price: $93.60

MAA Member Price: $105.30

# Local and Global Methods in Algebraic Geometry

Share this page *Edited by *
*Nero Budur; Tommaso de Fernex; Roi Docampo; Kevin Tucker*

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.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry and related fields.

# Table of Contents

## Local and Global Methods in Algebraic Geometry

- Cover Cover11
- Title page iii4
- Contents vii8
- Preface ix10
- Scientific program xi12
- Some remarks on the work of Lawrence Ein 114
- Contractible curves on a rational surface 922
- On the canonical map of some surfaces isogenous to a product 3346
- 1. Introduction and state of the art on canonical surfaces of high degree in \PP³,\PP⁴,\PP⁵ 3447
- 2. Representations yielding an affine, respectively a projective embedding, of a finite group 𝐺 3649
- 3. Canonical maps of Galois coverings and of surfaces isogenous to a product 4558
- 4. Surfaces with record winning high canonical degree 4861
- 5. New double canonical surfaces 5568
- References 5669

- Degeneration of differentials and moduli of nodal curves on 𝐾3 surfaces 5972
- Weak Brill-Noether for rational surfaces 8194
- Excellence in prime characteristic 105118
- Motivic zeta functions and infinite cyclic covers 117130
- 1. Introduction 117130
- 2. Infinite cyclic cover of finite type 118131
- 3. Motivic infinite cyclic zeta functions 120133
- 4. Relation with the Denef-Loeser motivic zeta function 135148
- 5. Further specializations of the motivic infinite cyclic zeta function 136149
- 6. Motivic zeta functions for arbitrary divisors. Relation to the monodromy conjecture 137150
- References 139152

- Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun 143156
- A strongly geometric general residual intersection 197210
- Quadratic solutions of quadratic forms 211224
- 1. Surfaces containing many circles 220233
- 2. Maps of \p¹ to quadrics 222235
- 3. Rational curves on quadrics 225238
- 4. Degenerate maps of \p² 228241
- 5. Veronese surfaces in quadric 4-folds 232245
- 6. Quadratic maps up to coordinate changes 235248
- 7. Quadrics of dimension ≥5 238251
- 8. Orthogonal Grassmannians 239252
- 9. Symmetric squares of orthogonal Grassmannians 244257
- References 247260

- Non-Cohen-Macaulay canonical singularities 251264
- Full cones swept out by minimal rational curves on irreducible Hermitian symmetric spaces as examples of varieties underlying geometric substructures 261274
- 1. Introduction and motivation 261274
- 2. Background materials and results 268281
- 3. Sub-VMRTs structures modeled on full cones of minimal rational curves in the Hermitian symmetric case 270283
- 4. Algebraicity of germs of sub-VMRT structures modeled on certain full cones of minimal rational curves 272285
- 5. Intrinsically flat sub-VMRT structures modeled on certain full cones of minimal rational curves 277290
- 6. Examples of non-standard sub-VMRT structures modeled on full cones of rational curves 280293
- 7. Concluding Remarks 281294
- References 283296

- A boundedness conjecture for minimal log discrepancies on a fixed germ 287300
- 1. Introduction 287300
- 2. Minimal log discrepancies: definition and basic facts 289302
- 3. Generic limits: bounding the order of the ideal of the point 292305
- 4. A proof of the conjecture in dimension 2 297310
- 5. A proof of the conjecture in the monomial case 300313
- 6. Connection with ACC 301314
- 7. Three equivalent conjectures 303316
- References 306319

- The Wahl map of one-nodal curves on K3 surfaces 307320
- Skoda’s ideal generation from vanishing theorem for semipositive Nakano curvature and Cauchy-Schwarz inequality for tensors 317330
- Introduction 317330
- 1. Algebraic Formulation and Application of Skoda’s Ideal Generation 319332
- 2. Cauchy-Schwarz Inequality for Tensors 322335
- 3. Nakano Curvature of Bundle and Twisting by Metric of Trivial Line Bundle 325338
- 4. Vanishing Theorem and Solution of ∂ Equation for Nonnegative Nakano Curvature 328341
- 5. Proof of Skoda’s Result on Ideal Generation 331344
- 6. Variants of Skoda’s Ideal Generation 334347
- 7. Comparison with Original Proof of Skoda’s Ideal Generation 336349
- References 338351

- Hyper-Kähler compactification of the intermediate Jacobian fibration of a cubic fourfold: The twisted case 341354
- Back Cover Back Cover1370