Intersection theory on Deligne-Mumford compactifications
Intersection theory using Adams operations.
Intersections of higher weight cycles and modular forms
Intersections of Projective Varieties and Generic Projections.
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].
Introduction à l’étude globale des tissus sur une surface holomorphe
Beaucoup de concepts sur les tissus n’ont été étudiés que localement. Il apparaît que certains d’entre eux se laissent globaliser, mais pas toujours de façon immédiate. Le premier objectif de cet article est de préciser à chaque fois ce qu’il en est, et de mettre en place les outils utiles à une étude globale des tissus sur une surface holomorphe arbitraire, et en particulier sur le plan projectif complexe . Certains concepts nouveaux vont alors apparaître, tels le type (ou le degré si ), la...
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...
Invariante Divisoren und Schnitthomologie von torischen Varietäten
In this article, we complete the interpretation of groups of classes of invariant divisors on a complex toric variety X of dimension n in terms of suitable (co-) homology groups. In [BBFK], we proved the following result (see Satz 1 below): Let and denote the groups of classes of invariant Cartier resp. Weil divisors on X. If X is non degenerate (i.e., not equivariantly isomorphic to the product of a toric variety and a torus of positive dimension), then the natural homomorphisms and are...
Irreducibility and monodromy of some families of linear series
Irreducibility of some families of linear series with Brill-Noether number. I
Irreducibility of the Space of Mathematical Instanton Bundles with Rank 2 and c2 = 4.
Irreducible Components of the Chow Scheme of Space Curves.
Isolated intersection multiplicity and regular separation of analytic sets
An isolated point of intersection of two analytic sets is considered. We give a sharp estimate of their regular separation exponent in terms of intersection multiplicity and local degrees.