The degrees of certain strata of the dual variety
The Denef-Loeser series for toric surface singularities.
Let H denote the set of formal ares going through a singular point of an algebraic variety V defined over an algebraically closed field k of charactcristic zcro. In the late sixties, J, Nash has observed that for any nonnegative integer s, the set js(H) of s-jets of ares in H is a constructible subset of some affine space. Recently (1999), J. Denef and F. Loeser have proved that the Poincaré series associated with the image of js(H) in some suitable localization of the Grothendieck ring of algebraic...
The density of rational and integral points on algebraic varieties
The density of S-integral points in projective space with respect to a quadric
The determinant line bundle over moduli spaces of instantons on abelian surfaces.
The Deuring-Safarevic Formula Revisited.
The diffeomorphism classification of non-simply connected Dolgachev surfaces.
The differential Galois theory of regular singular p-adic differential equations.
The differential spectrum of a ring
The (dimension + 2)-secant Lemma.
The dimension of certain catalecticant varieties.
The dimension of some affine Deligne–Lusztig varieties
The dimension of the Chow variety of curves
The dimension of the derived category of elliptic curves and tubular weighted projective lines
We show that the dimension of the derived category of an elliptic curve or a tubular weighted projective line is one. We give explicit generators realizing this number, and show that they are in a certain sense minimal.
The Diophantine equation f(x) = g(y)
The directional dimension of subanalytic sets is invariant under bi-Lipschitz homeomorphisms
Let be a set-germ at such that . We say that is a direction of at if there is a sequence of points tending to such that as . Let denote the set of all directions of at .Let be subanalytic set-germs at such that . We study the problem of whether the dimension of the common direction set, is preserved by bi-Lipschitz homeomorphisms. We show that although it is not true in general, it is preserved if the images of and are also subanalytic. In particular if two subanalytic...
The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives
We connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.
The discriminant of a real simple singularity
The Discriminants of a Series of Unimodular Singularities of Space Curves.
The discriminants of curves of genus 2