The moduli space M g of curves of fixed genus g that is, the algebraic variety that parametrizes all curves of genus g is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.

Autorentext
Dr. Carel Faber ist am Max-Planck-Institut für Mathematik in Bonn tätig.

Klappentext

The moduli space Mg of curves of fixed genus g - that is, the algebraic variety that parametrizes all curves of genus g - is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.

Inhalt
Distribution of rational points and Kodaira dimension of fiber products.- How many rational points can a curve have?.- Quantum cohomology of rational surfaces.- Quantum intersection rings.- Mirror symmetry and elliptic curves.- A generalized Jacobi theta function and quasimodular forms.- Boundary behaviour of Hurwitz schemes.- Operads and moduli spaces of genus 0 Riemann surfaces.- Resolution of diagonals and moduli spaces.- The Chow ring of the moduli space of curves of genus 5.- The cohomology of algebras over moduli spaces.- Enumeration of rational curves via torus actions.- Cellular decompositions of compactified moduli spaces of pointed curves.- Generating functions in algebraic geometry and sums over trees.- Holomorphicity and non-holomorphicity in N = 2 supersymmetric field theories.- An arithmetic problem in surface geometry.- An orbifold partition of $$ \bar M_g^n $$.- Moduli of curves with non-abelian level structure.- Q-structure of conformal field theory with gauge symmetries.- On the cohomology of moduli spaces of rank two vector bundles over curves.