1,037 research outputs found
Lines on projective varieties and applications
The first part of this note contains a review of basic properties of the
variety of lines contained in an embedded projective variety and passing
through a general point. In particular we provide a detailed proof that for
varieties defined by quadratic equations the base locus of the projective
second fundamental form at a general point coincides, as a scheme, with the
variety of lines. The second part concerns the problem of extending embedded
projective manifolds, using the geometry of the variety of lines. Some
applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added;
typos correcte
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 Zariski-Lipman conjecture for normal algebraic surfaces
We consider the Zariski-Lipman Conjecture on free module of derivations for
algebraic surfaces. Using the theory of non-complete algebraic surfaces, and
some basic results about ruled surfaces, we will prove the conjecture for
several classes of affine and projective surfaces.Comment: Final version; to appear in Jour. London Math. So
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