Some remarks on varieties with degenerate Gauss image

We consider projective varieties with degenerate Gauss image whose focal hypersurfaces are non-reduced schemes. Examples of this situation are provided by the secant varieties of Severi and Scorza varieties. The Severi varieties are moreover characterized by a uniqueness property.Comment: 9 pages, to be published in Pacific Journal of Mathematic

Stable cohomology of spaces of non-singular hypersurfaces

We prove that the rational cohomology of the space of non-singular complex homogeneous polynomials of degree d in a fixed number of variables stabilizes to the cohomology of the general linear group for d sufficiently large.Comment: 11 pages; v3: stabilization range made explicit, proof of Lemma 3 corrected and expande

Cohomology of the second Voronoi compactification of A_4

In this paper we compute the cohomology groups of the second Voronoi compactification of the moduli space of abelian fourfolds in all degrees with the exception of the middle degree 10. We also compute the cohomology groups of the perfect cone compactification in degree < 10. The main tool is the investigation of the strata of the compactification corresponding to semi-abelic varieties with constant torus rank.Comment: v2: 41 pages, mostly expository change

On projective varieties of dimension n+k covered by k-spaces

We study families of linear spaces in projective space whose union is a proper subvariety X of the expected dimension. We establish relations between configurations of focal points and existence or non-existence of a fixed tangent space to X along a general element of the family. We apply our results to the classification of ruled 3-dimensional varieties.Comment: To be published in Illinois Journal of Mathematic

Locally trivial families of hyperelliptic curves: the geometry of the Weierstrass scheme

In this paper we describe some geometrical properties of the Weierstrass scheme of locally trivial hyperelliptic fibrations.Comment: Correction of some minor error

The rational cohomology of \Mbar_4

We present two approaches to the study of the cohomology of moduli spaces of curves. Together, they allow us to compute the rational cohomology of the moduli space \Mbar_4 of stable complex curves of genus 4, with its Hodge structure.Comment: 28 pages. Changes mainly of notational and expository nature. The published paper is available at http://www.springerlink.co