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

• M. Atiyah -- Physics and geometry: A look at the last twenty years
• F. Hirzebruch -- Complex cobordism and the elliptic genus
• G. Banaszak, W. Gajda, and P. Krasoń -- On Galois cohomology of some \(p\)-adic representations and étale \(K\)-theory of curves
• G. Barthel, J.-P. Brasselet, K.-H. Fieseler, and L. Kaup -- Equivariant intersection cohomology of toric varieties
• E. Bayer-Fluckiger -- Lattices and number fields
• F. Campana -- \(\mathcal G\)-connectedness of compact Kähler manifolds. I
• F. Catanese -- Singular bidouble covers and the construction of interesting algebraic surfaces
• P. B. Cohen -- Quantum statistical mechanics and number theory
• H. Esnault and E. Viehweg -- Semistable bundles on curves and irreducible representations of the fundamental group
• G. Faltings -- Does there exist an arithmetic Kodaira-Spencer class?
• E. Getzler -- The Virasoro conjecture for Gromov-Witten invariants
• K. Hulek, I. Nieto, and G. K. Sankaran -- Degenerations of (1,3) abelian surfaces and Kummer surfaces
• Y. Kawamata -- On the extension problem of pluricanonical forms
• S. Kleiman and R. Piene -- Enumerating singular curves on surfaces
• H. Kurke and A. Matuschke -- On the structure of moduli spaces of framed vector bundles on rational and ruled surfaces
• A. Langer -- A note on \(k\)-jet ampleness on surfaces
• A. Lascoux -- About the "\(y\)" in the \(\chi_y\)-characteristic of Hirzebruch
• T. Shioda -- The splitting field of Mordell-Weil lattices
• M. Teicher -- Hirzebruch surfaces: Degenerations, related braid monodromy, Galois covers
• M.-F. Vignéras -- Intégrales orbitales modulo \(l\) pour un groupe réductif p-adique
• A. Weber -- A morphism of intersection homology and Hard Lefschetz
• S. Yokura -- On characteristic classes of complete intersections