The dimension of certain catalecticant varieties.
The dimension of some affine Deligne–Lusztig varieties
The discriminants of curves of genus 2
The distribution of bidegrees of smooth surfaces in Gr (1, P3).
The duals of generic hypersurfaces.
The Ehrhart polynomial of a lattice -simplex.
The equations of space curves on a quadric.
The homogeneous ideals of curves in a double plane have been studied by Chiarli, Greco, Nagel. Completing this work we describe the equations of any curve that is contained in some quadric. As a consequence, we classify the Hartshorne-Rao modules of such curves.
The Euler characteristic of varieties realized as the complete intersection of toric hypersurfaces.
The existence of equivariant pure free resolutions
Let be a polynomial ring in variables and let be a strictly increasing sequence of integers. Boij and Söderberg conjectured the existence of graded -modules of finite length having pure free resolution of type in the sense that for the -th syzygy module of has generators only in degree .This paper provides a construction, in characteristic zero, of modules with this property that are also -equivariant. Moreover, the construction works over rings of the form where is a polynomial...
The Fixed Point Subvarieties of Unipotent Transformations on Generalized Flag Varieties and the Green Functions. Combinatorial and Cohomological Treatments Centering GLn.
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 Genus of Curves in P4 verifying certain Flag conditions.
The Geometry of Representations of Am .
The geometry of the space of Cauchy data of nonlinear PDEs
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...
The Gorenstein Property Depends on Characteristic
The Grothendieck group of GL(F)×GL(G)-equivariant modules over the coordinate ring of determinantal varieties
The Hasse principle for homogeneous spaces.
The Hasse problem for rational surfaces.
The height function on the 2-dimensional cohomology of a flag manifold.
The Hilbert function of generic plane sections of curves of IP3.