Related papers: Seshadri constants on surfaces with Picard number …

The purpose of this paper is to explicitly compute the Seshadri constants of all ample line bundles on fake projective planes. The proof relies on the theory of the Toledo invariant, and more precisely on its characterization of…

We prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $\det(E)$). This result is a higher-rank version of a theorem…

In the first part of this paper we give a survey of classical results on Kummer surfaces with Picard number 17 from the point of view of lattice theory. We prove ampleness properties for certain divisors on Kummer surfaces and we use them…

Motivated by asymptotic phenomena of moduli spaces of higher rank stable sheaves on algebraic surfaces, we study the Picard number of the moduli space of one-dimensional stable sheaves supported in a sufficiently positive divisor class on a…

Let $X$ be an irreducible smooth geometrically integral projective surface over a field. In this paper we give an effective bound in terms of the Neron--Severi rank $\rho(X)$ of $X$ for the number of irreducible curves $C$ on $X$ with…

We first show that the union of a projective curve with one of its extremal secant lines satisfies the linear general position principle for hyperplane sections. We use this to give an improved approximation of the Betti numbers of curves…

Lasell and Ramachandran show that the existence of rational curves of positive self-intersection on a smooth projective surface $X$ implies that all the finite dimensional linear representations of the fundamental group $\pi_1(X)$ are…

Let $R$ be a ring generated by $l$ elements with stable range $r$. Assume that the group $EL_d(R)$ has Kazhdan constant $\epsilon_0>0$ for some $d > r $. We prove that there exist $\epsilon(\epsilon_0,l) >0$ and $k \in N$, s.t. for every $n…

In this paper we give for all $n \geq 2$, d>0, $g \geq 0$ necessary and sufficient conditions for the existence of a pair (X,C), where X is a K3 surface of degree 2n in $\matbf{P}^{n+1}$ and C is a smooth (reduced and irreducible) curve of…

We study constant mean curvature surfaces in the three-dimensional Heisenberg group. We prove that a constant mean curvature surface in a neighborhood of non-umbilic point is described by some solution of a sinh-Gordon equation subject to a…

This paper is about the family of smooth quartic surfaces $X \subset \mathbb{P}^3$ that are invariant under the Heisenberg group $H_{2,2}$. For a very general such surface $X$, we show that the Picard number of $X$ is 16 and determine its…

Let X be a smooth double cover of a geometrically ruled surface defined over a separably closed field of characteristic different from 2. The main result of this paper is a finite presentation of the 2-torsion in the Brauer group of X with…

Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant C such that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at most one…

If $X$ is a non-degenerate vector field on ${\bf R}$ and $H=-X^2$ we examine conditions for the closure of $H$ to generate a continuous semigroup on $L_\infty$ which extends to the $L_p$-spaces. We give an example which cannot be extended…

We extend the concept of Segre's Invariant to vector bundles on a surface $X$. For $X=\mathbb{P}^2$ we determine what numbers can appear as the Segre Invariant of a rank $2$ vector bundle with given Chern's classes. The irreducibility of…

Assuming projective determinacy, we extend Spector's strong version of the Spector-Gandy Theorem to all odd levels of the projective hierarchy: Theorem. For every space $X$ which is a finite product of the natural numbers $N$ and Baire…

We prove the so-called Severi inequality, stating that the invariants of a minimal smooth complex projective surface of maximal Albanese dimension satisfy: K^2_S >= 4\chi(S).

Let $E$ be a vector bundle on a smooth complex projective variety $X$. We study the family of sections $s_t\in H^0(E\otimes L_t)$ where $L_t\in Pic^0(X)$ is a family of topologically trivial line bundle and $L_0=\mathcal O_X,$ that is, we…

We use Harer's stability theorem to give another proof of his fundamental theorem: The rank of the Picard group of the moduli space of smooth projective curves of genus g > 2 equals one.

We give asymptotic bounds for the optimal Lipschitz constants for the systole map from the Teichmuller space to the curve complex. We give similar results to those known for closed surfaces in the cases when the genus is fixed or the ratio…