Related papers: On Chern ratios for surfaces with ample cotangent …

Projective varieties with ample cotangent bundle satisfy many notions of hyperbolicity, and one goal of this paper is to discuss generalizations to quasi-projective varieties. A major hurdle is that the naive generalization fails, i.e. the…

In order to count the number of smooth cubic hypersurfaces tangent to a prescribed number of lines and passing through a given number of points, we construct a compactification of their moduli space. We term the latter a…

In this paper, we investigate Murre's conjectures on the structure of rational Chow groups and exhibit explicit Chow--Kuenneth projectors for some examples. More precisely, the examples we study are the varieties which have a nef tangent…

We analyze surface patches with a corner that is rounded in the sense that the partial derivatives at that point are antiparallel. Sufficient conditions for $G^1$ smoothness are given, which, up to a certain degenerate case, are also…

In this paper we develop the geometry of bounded Fr\'echet manifolds. We prove that a bounded Fr\'echet tangent bundle admits a vector bundle structure. But the second order tangent bundle $T^2M$ of a bounded Fr\'echet manifold $M$, becomes…

We proved that the union of rational curves is dense on a very general K3 surface and the union of elliptic curves is dense in the 1st jet space of a very general K3 surface, both in the strong topology.

We provide very general symmetrization theorems in arbitrary dimension and codimension, in products, warped products, and certain fiber bundles such as lens spaces, including Steiner, Schwarz, and spherical symmetrization and admitting…

If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an…

We study the topology of exact and Stein fillings of the canonical contact structure on the unit cotangent bundle of a closed surface $\Sigma_g$, where $g$ is at least 2. In particular, we prove a uniqueness theorem asserting that any Stein…

We formulate a tropical analogue of Grothendieck's section conjecture: that for every stable graph G of genus g>2, and every field k, the generic curve with reduction type G over k satisfies the section conjecture. We prove many cases of…

We give the classification of globally generated vector bundles of rank $2$ on a smooth quadric surface with $c_1\le (2,2)$ in terms of the indices of the bundles, and extend the result to arbitrary higher rank case. We also investigate…

In this paper, I construct Chern classes in the rigid cohomology of P. Berthelot. We start by constructing Chern classes for proper varieties. To prove all the properties we have to reinterpret the construction in a crystalline way. Then we…

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…

Let $G$ be the topological fundamental group of a given nonsingular complex projective surface. We prove that the Chern slopes $c_1^2(S)/c_2(S)$ of minimal nonsingular projective surfaces of general type $S$ with $\pi_1(S) \simeq G$ are…

Call a curve $C \subset \mathbb{P}^2$ defined over $\mathbb{F}_q$ transverse-free if every line over $\mathbb{F}_q$ intersects $C$ at some closed point with multiplicity at least 2. In 2004, Poonen used a notion of density to treat Bertini…

In this work we describe the Chen-Ruan cohomology of the moduli stacks of smooth and stable genus 2 pointed curves, and its algebraic counterpart: the stringy Chow ring. In the first half of the paper we compute the additive structure of…

A study of the relation between the electrostatic charge density at a point on a conducting surface and the curvature of the surface (at that point) is presented. Two major scientific literature on this topic are reviewed and the apparent…

In this short note we will show that every homogeneous strictly nef vector bundle on a complex flag variety is ample. Following this, we consider whether ampleness of a bundle on an abelian variety can be tested on curves.

A cocycle $\Omega: P \times G \to H$ taking values in a Lie group $H$ for a free right action of $G$ on $P$ defines a principal bundle $Q$ with the structure group $H$ over $P/G.$ The Chern character of a vector bundle associated to $Q$…

We find, for all sufficiently large $n$ and each $k$, the maximum number of edges in an $n$-vertex graph which does not contain $k+1$ vertex-disjoint triangles. This extends a result of Moon [Canad. J. Math. 20 (1968), 96-102] which is in…