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