Related papers: Biduality and Reflexivity in Positive Characterist…
We consider the following conjecture: if X is a smooth projective variety over a field of characteristic zero, then there is a dense set of reductions X_s of X to positive characteristic such that the action of the Frobenius morphism on the…
A subvariety of a complex projective space has a well-known dual variety, which is the set of its tangent hyperplanes. The purpose of this paper is to generalise this notion for a subvariety of a quite general partial flag variety. A…
Here we investigate the birational geometry of projective varieties of arbitrary dimension having defective higher secant varieties. We apply the classical tool of tangential projections and we determine natural conditions for uniruledness,…
Given an invertible sheaf on a fibre space between projective varieties of positive characteristic, we show that fibrewise semi-ampleness implies relative semi-ampleness. The same statement fails in characteristic zero.
A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main result characterizes C-rigid complexes. Specialized to the case when C is the relative…
We consider the following conjecture: if X is a smooth projective variety over a field of characteristic zero, then there is a dense set of reductions X_s to positive characteristic such that the action of the Frobenius morphism on the top…
In continuation of the paper [3], we discuss various consequences of Hahn-Banach theorem for bounded b-linear functional in linear n-normed space and describe the notion of reflexivity of linear n-normed space with respect to bounded…
We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector bundle adjunction. We use methods and…
Reflexive homology and dihedral homology are the homology theories associated to the reflexive and dihedral crossed simplicial groups respectively. The former has recently been shown to capture interesting information about…
Based on a recent extension theorem for reflexive differential forms, that is, regular differential forms defined on the smooth locus of a possibly singular variety, we study the geometry and cohomology of sheaves of reflexive…
Contrary to recent claims in the literature, a simple test for reflection positivite, which we call perturbative reflection positivity in the coincidence limit, is shown to be satisfied for nonlocal field theories. Particular attention is…
It is shown that the recently proposed target space duality for (0,2) models is not limited to models admitting a Landau-Ginzburg description. By studying some generic examples it is established for the broader class of vector bundles over…
We study differential forms invariant under a finite reflection group over a field of arbitrary characteristic. In particular, we prove an analogue of Saito's freeness criterion for invariant differential 1-forms. We also discuss how…
We prove that the weak Hilbert property ascends along a morphism of varieties over an arbitrary field of characteristic zero, under suitable assumptions.
We survey results concerning behavior of positivity of line bundles and possible vanishing theorems in positive characteristic. We also try to describe variation of positivity in mixed characteristic. These problems are very much related to…
We prove basic facts about reflexivity in derived categories over noetherian schemes; and about related notions such as semidualizing complexes, invertible complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity with…
We investigate when the tangent bundle of a projective manifold has a non-trivial first order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.
Given a Banach space. We show that its three times dual space can be written as a direct sum. Then being one of the sumands null is a necessary and sufficient condition for the dual space to be reflexive. We end with an application of this…
The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological…
We introduce a notion of constructibility for \'etale sheaves with torsion coefficients over a suitable class of adic spaces. This notion is related to the classical notion of constructibility for schemes via the nearby cycles functor. We…