arXiv subjects

Barbara Fantechi

Publications and source records attributed to Barbara Fantechi.

21 records · Page 2Linked to original sources

arXiv1997

Euler number of the compactified Jacobian and multiplicity of rational curves

We show that the Euler number of the compactified Jacobian of a rational curve $C$ with locally planar singularities is equal to the multiplicity of the $δ$-constant stratum in the base of a semi-universal deformation of $C$. In particular, the multiplicity assigned by Yau, Zaslow and Beauville to a rational curve on a K3 surface $S$ coincides with the multiplicity of the normalisation map in the moduli space of stable maps to $S$.

alg-geom↗

arXiv1995

On the Hilbert scheme of curves in higher-dimensional projective space

In this paper we prove that, for any $n\ge 3$, there exist infinitely many $r\in \N$ and for each of them a smooth, connected curve $C_r$ in $¶^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme $\hilb(¶^r)$. This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type.

alg-geom↗

arXiv1994

Automorphisms and moduli spaces of varieties with ample canonical class via deformations of abelian covers

By a recent result of Viehweg, projective manifolds with ample canonical class have a coarse moduli space, which is a union of quasiprojective varieties. In this paper, we prove that there are manifolds with ample canonical class that lie on arbitrarily many irreducible components of the moduli; moreover, for any finite abelian group $G$ there exist infinitely many components $M$ of the moduli of varieties with ample canonical class such that the generic automorphism group $G_M$ is equal to $G$. In order to construct the examples, we use abelian covers, i.e. Galois cover whose Galois group is finite and abelian. We prove two results about abelian covers: first, that if the building data are sufficiently ample, then the natural deformations surject on the Kuranishi family of $X$; second, that if the building data are sufficiently ample and generic, then $Aut(X)=G$.

alg-geom↗