The discriminants of curves of genus 2
The divisor of curves with a vanishing theta-null
The duality of cusp singularities.
The Euler characteristic of varieties realized as the complete intersection of toric hypersurfaces.
The Euler number of the normalization of an algebraic threefold with ordinary singularities
By a classical formula due to Enriques, the Euler number χ(X) of the non-singular normalization X of an algebraic surface S with ordinary singularities in P³(ℂ) is given by χ(X) = n(n²-4n+6) - (3n-8)m + 3t - 2γ, where n is the degree of S, m the degree of the double curve (singular locus) of S, t is the cardinal number of the triple points of S, and γ the cardinal number of the cuspidal points of S. In this article we shall give a similar formula for an algebraic threefold with ordinary singularities...
The Euler series of restricted Chow varieties
The explicit reciprocity law and the cohomology of Fontaine-Messing
The Formal Hodge Filtration.
The generalized Hodge and Bloch conjectures are equivalent for general complete intersections
We prove that Bloch’s conjecture is true for surfaces with obtained as -sets of a section of a very ample vector bundle on a variety with “trivial” Chow groups. We get a similar result in presence of a finite group action, showing that if a projector of the group acts as on holomorphic -forms of , then it acts as on -cycles of degree of . In higher dimension, we also prove a similar but conditional result showing that the generalized Hodge conjecture for general implies the...
The generalized Hodge conjecture for stably nondegenerate abelian varieties
The gonality of general smooth curves with a prescribed plane nodal model.
The gonality of smooth curves with plane Models.
The Grothendieck group of GL(F)×GL(G)-equivariant modules over the coordinate ring of determinantal varieties
The Grothendieck-Riemann-Roch theorem for group scheme actions
The hard Lefschetz theorem and the topology of semismall maps
The Hilbert Function of curves on certain smooth quartic surfaces.
The Hilbert Modular Surface of a Real Quadratic Field.
The Hilbert Scheme of Buchsbaum space curves
We consider the Hilbert scheme of space curves with homogeneous ideal and Rao module . By taking suitable generizations (deformations to a more general curve) of , we simplify the minimal free resolution of by e.g making consecutive free summands (ghost-terms) disappear in a free resolution of . Using this for Buchsbaum curves of diameter one ( for only one ), we establish a one-to-one correspondence between the set of irreducible components of that contain and a set of minimal...
The Hilbert scheme of space curves of small diameter
This paper studies space curves of degree and arithmetic genus , with homogeneous ideal and Rao module , whose main results deal with curves which satisfy (e.g. of diameter, ). For such curves we find necessary and sufficient conditions for unobstructedness, and we compute the dimension of the Hilbert scheme, , at under the sufficient conditions. In the diameter one case, the necessary and sufficient conditions coincide, and the unobstructedness of turns out to be equivalent to the...
The Hilbert schemes of degree three curves