Effective Estimates for Unirationality.
We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit bound on the degree.
Principally polarized abelian surfaces are the Jacobians of smooth genus 2 curves or of stable genus 2 curves of special type. In [S] we studied equations describing Kummer surfaces in the case of an irreducible principal polarization on the abelian surface. The aim of this note is to give a treatment of the second case. We describe intermediate Kummer surfaces coming from abelian surfaces carrying a product principal polarization. In Proposition 12 we give explicit equations of these surfaces in...
De Concini and Procesi have defined the wonderful compactification of a symmetric space where is a complex semisimple adjoint group and the subgroup of fixed points of by an involution . It is a closed subvariety of a Grassmannian of the Lie algebra of . In this paper we prove that, when the rank of is equal to the rank of , the variety is defined by linear equations. The set of equations expresses the fact that the invariant alternate trilinear form on vanishes on the -eigenspace...
Let be an affine conical factorial variety over an algebraically closed field of characteristic zero. We consider equidimensional and stable algebraic actions of an algebraic torus on compatible with the conical structure. We show that such actions are cofree and the nullcones of associated with them are complete intersections.