Related papers: What determines a variety?
We consider a relation between local and global characteristics of a differential algebraic variety. We prove that dimension of tangent space for every regular point of an irreducible differential algebraic variety coincides with dimension…
We study the normal map for plane projective curves, i.e., the map associating to every regular point of the curve the normal line at the point in the dual space. We first observe that the normal map is always birational and then we use…
Betten and Riesinger have shown that Clifford parallelism on real projective space is the only topological parallelism that is left invariant by a group of dimension at least 5. We improve the bound to 4. Examples of different parallelisms…
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…
We investigate unital, subtractive and strongly unital regular categories with enough projectives and give characterizations of their projective covers. The categorical equation "strongly unital = unital + subtractive" is explored: this…
Given a variety defined over a field of characteristic zero and an algebraically integrable foliation of corank less than or equal to two, we show the existence of a categorical quotient, defined on the non-empty open set of stable points,…
For many classical moduli spaces of orthogonal type there are results about the Kodaira dimension. But nothing is known in the case of dimension greater than 19. In this paper we obtain the first results in this direction. In particular the…
We develop, for an l-adic etale sheaf on a complete trait of characteristic p>0, the notion of characteristic variety. Our approach, inspired by the microlocal analysis of Kashiwara and Schapira, is a complement to our ramification theory…
We describe classes of toric varieties of codimension 2 which are either minimally defined by 3 binomial equations over any algebraically closed field, or are set-theoretic complete intersections in exactly one positive characteristic.
Gray-Vanhecke conjectured that the volumes of small geodesic balls could determine if the manifold is a space form, and provided a proof for the compact 4-dimensional manifold, and some cases. In this paper, similar results for the…
We study the subvariety of singular sections, the discriminant, of a base point free linear system $|L|$ on a smooth toric variety $X$. On one hand we describe pairs $(X,L)$ for which the discriminant is of low dimension. Precisely, we…
We determine all Chern numbers of smooth complex projective varieties of dimension at least four which are determined up to finite ambiguity by the underlying smooth manifold. We also give an upper bound on the dimension of the space of…
This paper explores various homological regularity phenomena (in the sense of Auslander) in category $\mathcal{O}$ and its several variations and generalizations. Additionally, we address the problem of determining projective dimension of…
A distinguished variety is a variety that exits the bidisk through the distinguished boundary. We show that Ando's inequality for commuting matrix contractions can be sharpened to looking at the maximum modulus on a distinguished variety,…
We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space $\left(X,\tau\right)$ is definably homeomorphic to an affine definable space…
We confirm Beauville's conjecture that claims that if the p-th exterior power of the tangent bundle of a smooth projective variety contains the p-th power of an ample line bundle, then the variety is either the projective space or the…
We give an upper bound on the topological complexity of varieties $\mathcal{V}$ obtained as complements in $\mathbb{C}^m$ of the zero locus of a polynomial. As an application, we determine the topological complexity of unordered…
In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map of Weingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type…
"Most" hypersurfaces in projective space are irreducible, and rather precise estimates are known for the probability that a random hypersurface over a finite field is reducible. This paper considers the parametrization of space curves by…
In this paper we prove a conjecture of Bryant, Griffiths, and Yang concerning the characteristic variety for the determined isometric embedding system. In particular, we show that the characteristic variety is not smooth for any dimension…