Cinzia Casagrande

Moduli of roots of line bundles on curves

We treat the problem of completing the moduli space for roots of line bundles on curves. Special attention is devoted to higher spin curves within the universal Picard scheme. Two new different constructions, both using line bundles on nodal curves as boundary points, are carried out and compared with pre-existing ones.

Combinatorial Properties of Stable Spin Curves

Abstract The geometry of the moduli space of stable spin curves is studied, with emphasis on its combinatorial properties. In this context, the standard graph-theoretic framework is not just a book-keeping device: some purely combinatorial results are proved, having moduli- theoretic applications. In particular, certain strata of the moduli space of stable curves are characterized by a (finite) set of integers, measuring the non-reducedness of the scheme of spin curves, and definable in purely graph-theoretical terms. Dedicated to Steven L. Kleiman on the occasion of his 60th birthday.

On covering and quasi-unsplit families of curves

Given a covering family

Toric Fano varieties and birational morphisms

V

ON THE PICARD NUMBER OF ALMOST FANO THREEFOLDS WITH PSEUDO-INDEX > 1

of effective 1-cycles on a complex projective variety

On the birational geometry of toric Fano 4-folds

X

On the Fano variety of linear spaces contained in two odd-dimensional quadrics

, we find conditions allowing to construct a geometric quotient

The number of vertices of a Fano polytope

q~: X \to Y

Contractible classes in toric varieties

, with

Sur une conjecture de Mukai

q