Related papers: Projective contact log varieties

Using a recent description of the geometric stability manifold, we show the geometric stability manifold associated to any smooth projective complex surface is contractible. We then use this result to demonstrate infinitely many new…

We discuss several numerical conditions for families of projective varieties or variations of Hodge structures.

We show that if a smooth projective curve $C\subset\mathbb P^3$ (over an algebraically closed field of characteristic zero) is Legendrian with respect to a contact structure (it is well known that a contact structure on $\mathbb P^3$ is…

A translation surface is a surface formed by identifying edges of a collection of polygons in the complex plane that are parallel and of equal length using only translations. We determined that the same circle packing can be realized on…

We prove that the canonical ring of a smooth projective variety is finitely generated.

Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications…

In this work we generalize the classical notion of a (compact) twistor line in the period domain of compact complex tori. We introduce two new types of lines, which are non-compact analytic curves in the period domain of complex tori. We…

We propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor…

We determine the structure of solvable Lie groups endowed with invariant stretched non-positive Weyl connections and find classes of solvable Lie groups admitting and not admitting such connections. In dimension 4 we fully classify solvable…

We investigate finite non-Abelian simple groups $G$ for which the projective cover of the trivial module coincides with the permutation module on a subgroup and classify all cases unless $G$ is of Lie type in defining characteristic.

Given a connected smooth projective surface X over the complex numbers, together with a simple normal crossings divisor D on it, we study finite normal covers Y of X that are unramified outside D. Given moreover a fibration of X onto a…

We study the projective models of complex K3 surfaces polarized by a line bundle L such that all smooth curves in |L| have non-general Clifford index. Such models are in a natural way contained in rational normal scrolls. We use this study…

We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.

We extend the injectivity theorem of Esnault and Viehweg to a class of non-normal log varieties, which contains normal crossings log varieties, and is closed under the operation of taking the $\LCS$ locus.

We construct a linearly normal smooth rational surface S of degree 11 and sectional genus 8 in the projective fivespace. Surfaces satisfying these numerical invariants are special, in the sense that $h^1(\mathscr{O}_S(1))>0$. Our…

In these notes we investigate the cone of nef curves of projective varieties, which is the dual cone to the cone of pseudo-effective divisors. We prove a structure theorem for the cone of nef curves of projective $\mathbb Q$-factorial klt…

We prove some classification results for tight contact structure in the 3-space, -ball and -sphere that are invariant with respect to some arbitrary involution, that is conjugated to the standard rotation around the x-axis. Unlike the…

We introduce and study the base locus and the strong base locus of a projective variety X. The base locus of X parametrizes configurations of smooth points of X where the span of the tangent spaces of X at these points intersects X at some…

Let $X$ be a connected smooth complex projective variety of dimension $n \geq 1$. Let $D$ be a simple normal crossing divisor on $X$. Let $G$ be a connected complex Lie group, and $E_G$ a holomorphic principal $G$-bundle on $X$. In this…

We prove rigidity of various types of holomorphic parabolic geometry on smooth complex projective varieties.