Ein globaler Starrheitssatz für Mumfordkurven.
Einfacher Zusammenhang der Hilbertschemata von Kurven im komplex-projektiven Raum.
Enumerative geometry of singular plane curves.
Equivalence of families of singular schemes on threefolds and on ruled fourfolds.
The main purpose of this paper is twofold. We first analyze in detail the meaningful geometric aspect of the method introduced in [12], concerning families of irreducible, nodal curves on a smooth, projective threefold X. This analysis gives some geometric interpretations not investigated in [12] and highlights several interesting connections with families of other singular geometric objects related to X and to other varieties. Then we use this method to study analogous problems for families of...
Equivariant counts of points of the moduli spaces of pointed hyperelliptic curves.
Erratum: “Curves on generic hypersurfaces”
Essential dimension of moduli of curves and other algebraic stacks
In this paper we consider questions of the following type. Let be a base field and be a field extension. Given a geometric object over a field (e.g. a smooth curve of genus ), what is the least transcendence degree of a field of definition of over the base field ? In other words, how many independent parameters are needed to define ? To study these questions we introduce a notion of essential dimension for an algebraic stack. Using the resulting theory, we give a complete answer to...
Euler characteristics of moduli spaces of curves
Let be the moduli space of -pointed Riemann surfaces of genus . Denote by the Deligne-Mumford compactification of . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of for any and such that .
Existence de faisceaux réflexifs de rang deux sur à bonne cohomologie
Existence, decomposition, and limits of certain Weierstrass points.