255 research outputs found
Variety of power sums and divisors in the moduli space of cubic fourfolds
We show that a cubic fourfold F that is apolar to a Veronese surface has the
property that its variety of power sums VSP(F,10) is singular along a K3
surface of genus 20. We prove that these cubics form a divisor in the moduli
space of cubic fourfolds and that this divisor is not a Noether-Lefschetz
divisor. We use this result to prove that there is no nontrivial Hodge
correspondence between a very general cubic and its VSP.Comment: 42 pages, expanded and revised version to appear in Documenta
Mathematic
Apolarity, Hessian and Macaulay polynomials
A result by Macaulay states that an Artinian graded Gorenstein ring R of
socle dimension one and socle degree b can be realized as the apolar ring of a
homogeneous polynomial f of degree b. If R is the Jacobian ring of a smooth
hypersurface g=0, then b is just equal to the degree of the Hessian polynomial
of g. In this paper we investigate the relationship between f and the Hessian
polynomial of g.Comment: 12 pages. Improved exposition, minor correction
Algorithms for Del Pezzo Surfaces of Degree 5 (Construction, Parametrization)
It is well known that every Del Pezzo surface of degree 5 defined over k is
parametrizable over k. In this paper we give an efficient construction for
parametrizing, as well as algorithms for constructing examples in every
isomorphism class and for deciding equivalence.Comment: 15 page
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