# Algebraic Geometry: Hirzebruch 70

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*Piotr Pragacz; Michał Szurek; Jarosław Wiśniewski*

This book presents the proceedings from the conference on algebraic geometry in honor of Professor Friedrich Hirzebruch's 70th Birthday. The event was held at the Stefan Banach International Mathematical Center in Warsaw (Poland). Topics covered in the book include intersection theory, singularities, low-dimensional manifolds, moduli spaces, number theory, and interactions between mathematical physics and geometry. Also included are articles from notes of two special lectures. The first, by Professor M. Atiyah, describes the important contributions to the field of geometry by Professor Hirzebruch. The second article contains notes from the talk delivered at the conference by Professor Hirzebruch. Contributors to the volume are leading researchers in the field.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry; physicists.

# Table of Contents

## Algebraic Geometry: Hirzebruch 70

- Contents vii8 free
- Preface ix10 free
- List of participants xi12 free
- List of lectures xiii14 free
- Physics and Geometry: a look at the last twenty years 116 free
- Complex cobordism and the elliptic genus 924
- On Galois cohomology of some p-adic representations and étale K -theory of curves 2338
- Equivariant intersection cohomology of toric varieties 4560
- Introduction 4661
- 0. Preliminaries 5065
- 1. Equivariant Cohomology of Toric Varieties 5166
- 2. The Equivariant Intersection Cohomology Sheaf 5570
- 3. Minimal Extension Sheaves 5671
- 4. Equivariantly Formal Toric Varieties and Pointwise Freeness of IHT. 5772
- 5. Local Minimal Extension Property of IHT. 6075
- 6. Some Results on Equivariantly Formal Fans 6378
- References 6782

- Lattices and number fields 6984
- G-connectedness of compact Kähler manifolds, I 85100
- Singular bidouble covers and the construction of interesting algebraic surfaces 97112
- Quantum statistical mechanics and number theory 121136
- Semistable bundles on curves and irreducible representations of the fundamental group 129144
- Does there exist an arithmetic Kodaira-Spencer class? 141156
- The Virasoro conjecture for Gromov-Witten invariants 147162
- Degenerations of (1,3) abelian surfaces and Kummer surfaces 177192
- On the extension problem of pluricanonical forms 193208
- Enumerating singular curves on surfaces 209224
- On the structure of moduli spaces of framed vector bundles on rational and ruled surfaces 239254
- A note on k-jet ampleness on surfaces 273288
- About the "y" in the Xy-characteristic of Hirzebruch 285300
- The splitting field of Mordell-Weil lattices 297312
- Hirzebruch surfaces: degenerations, related braid monodromy, Galois covers 305320
- Intégrates orbitales modulo l pour un groupe réductif p-adique 327342
- A morphism of intersection homology and hard Lefschetz 339354
- On characteristic classes of complete intersections 349364