Generalized Hodge classes on the moduli space of curves.
Genre des courbes algébriques dans l'espace projectif
Genre des courbes de l'espace projectif. II
Geometric linear normality for nodal curves on some projective surfaces
In questo lavoro si generalizzano alcuni risultati di [3] riguardanti la proprietà di alcune curve nodali, su superficie non-singolari in , di essere «geometricamente linearmente normali» (concetto che estende la ben nota proprietà di essere linearmente normale). Precisamente, per una data curva , irriducibile e dotata di soli punti nodali come uniche singolarità, che giace su una superfice proiettiva, non-singolare e linearmente normale, si determina un limite superiore «sharp» sul numero dei...
Géométrie formelle et géométrie algébrique
Gonality for stable curves and their maps with a smooth curve as their target
Here we study the deformation theory of some maps f: X → ℙr , r = 1, 2, where X is a nodal curve and f|T is not constant for every irreducible component T of X. For r = 1 we show that the “stratification by gonality” for any subset of [...] with fixed topological type behaves like the stratification by gonality of M g.
Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques.
Hauteurs canoniques sur l'espace de modules des fibrés stables sur une courbe algébrique
Hilbert scheme of smooth space curves
Hodge integrals and invariants of the unknot.
Hurwitz spaces of genus 2 covers of an elliptic curve.
Let E be an elliptic curve over a field K of characteristic not equal to 2 and let N > 1 be an integer prime to char(K). The purpose of this paper is to construct the (two-dimensional) Hurwitz moduli space H (E/K,N,2) which classifies genus 2 covers of E of degree N and to show that it is closely related to the modular curve X(N) which parametrizes elliptic curves with level-N-structure. More precisely, we introduce the notion of a normalized genus 2 cover of E/K and show that the corresponding...
Infinite Grassmannians and moduli spaces of G-bundles.
Intersection-theoretical computations on
In this paper we explore several concrete problems, all more or less related to the intersection theory of the moduli space of (stable) curves, introduced by Mumford [Mu 1].
Invariance of tautological equations I: conjectures and applications
The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, this framework gives an efficient algorithm to calculate all tautological equations using only finite-dimensional linear algebra. Other applications include the proofs of Witten’s conjecture on the relations between higher spin curves and Gelfand–Dickey hierarchy and Virasoro conjecture for target manifolds with conformal semisimple quantum cohomology, both for genus up to...
Invariant theory for and the rationality of
Invarianten der degenerierten Fasern in lokalen Familien von Kurven.
Invariants of plane algebraic curves via representations of the braid group.
Invertible cohomological field theories and Weil-Petersson volumes
We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande....
Irreducibility and monodromy of some families of linear series
Irreducibility of some families of linear series with Brill-Noether number. I