120 research outputs found
On universal Severi varieties of low genus K3 surfaces
We prove the irreducibility of universal Severi varieties parametrizing
irreducible, reduced, nodal hyperplane sections of primitive K3 surfaces of
genus g, with 3 \le g \le 11, g \neq 10.Comment: Some minor mistakes in the introductory paragraph 1.1 corrected. To
appear in Math.
Intrinsic pseudo-volume forms for logarithmic pairs
31 pagesInternational audienceWe study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic K-correspondences. We define an intrinsic logarithmic pseudo-volume form \Phi_{X,D} for every pair (X,D) consisting of a complex manifold X and a normal crossing Weil divisor, the positive part of which is reduced. We then prove that \Phi_{X,D} is generically non-degenerate when X is projective and K_X+D is ample. This result is analogous to the classical Kobayashi-Ochiai theorem. We also show the vanishing of \Phi_{X,D} for a large class of log-K-trivial pairs, which is an important step in the direction of the Kobayashi conjecture about infinitesimal measure hyperbolicity in the logarithmic case
Moduli of curves on Enriques surfaces
We compute the number of moduli of all irreducible components of the moduli
space of smooth curves on Enriques surfaces. In most cases, the moduli maps to
the moduli space of Prym curves are generically injective or dominant.
Exceptional behaviour is related to existence of Enriques--Fano threefolds and
to curves with nodal Prym-canonical model.Comment: Final version, to appear in Advances in Mathematic
On the locus of Prym curves where the Prym--canonical map is not an embedding
We prove that the locus of Prym curves of genus for
which the Prym-canonical system is base point free but the
Prym--canonical map is not an embedding is irreducible and unirational of
dimension .Comment: Minor modifications. Final version, accepted for publication in Arkiv
f\"or Matemati
The fundamental group of quotients of a product of curves
International audienceWe prove a structure theorem for the fundamental group of the quotient X of a product of curves by the action of a finite group G, hence for that of any resolution of the singularities of X
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