Related papers: Partially ample subvarieties of projective varieti…

In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables…

We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of…

Let X be a normal connected complex algebraic variety equipped with a semisimple complex representation of its fundamental group. Then, under a maximality assumption, we prove that the covering space of X associated to the kernel of the…

We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension.…

We define, for an arbitrary partially ordered set, a multi-variable polynomial generalizing the hook polynomial.

In some varieties of algebras one can reduce the question of finding most general unifiers (mgus) to the problem of the existence of unifiers that fulfill the additional condition called projectivity. In this paper we study this problem for…

Let G be a connected reductive group and X an equivariant compactifiction of G. In X, we study generalised and opposite generalised Schubert varieties, their intersections called generalised Richardson varieties and projected generalised…

We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.

We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteration of the map, while the whole subvariety is not. Several…

We study complex analytic (possibly singular) projective connections on the plane. We characterize some of them in terms of their families of integral curves. We also give a beginning of classification of second order odes polynomial in the…

Let $f: Y\to X$ be a morphism between smooth complex quasi-projective varieties and $Z$ be the closure of $f(Y)$ with $\iota: Z\to X$ the inclusion map. We prove that a. for any field $K$, there exist finitely many semisimple…

One version of the classical Lefschetz hyperplane theorem states that for $U \subset \mathbb P^n$ a smooth quasi-projective variety of dimension at least $2$, and $H \cap U$ a general hyperplane section, the resulting map on \'etale…

Let $X$ be a quasi-affine algebraic variety isomorphic to the complement of a closed subvariety of dimension at most $n-3$ in $\C^n$. We find some conditions under which an isomorphism of two closed subvarieties of $X$ can be extended to an…

We prove a general inequality for estimating the number of points of arbitrary complete intersections over a finite field. This extends a result of Deligne for nonsingular complete intersections. For normal complete intersections, this…

We characterize integral homology classes of the product of two projective planes which are representable by a subvariety.

Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite regular generator which is regularly projective (its hom-functor preserves regular epimorphisms).…

We give the first examples of nef line bundles on smooth projective varieties over finite fields which are not semi-ample. More concretely, we find smooth curves on smooth projective surfaces over finite fields such that the normal bundle…

We study the cones of q-ample divisors on smooth complex varieties. In favourable cases, we identify a part where the closure of this cone and the nef cone have the same boundary. This is especially interesting for Fano (or almost Fano)…

Let $X$ be an irreducible projective variety and $f$ a morphism $X \rightarrow \mathbb{P}^n$. We give a new proof of the fact that the preimage of any linear variety of dimension $k\ge n+1-\dim f(X)$ is connected. We prove that the…

We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.