Related papers: Bounding cohomology on a smooth projective surface

To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A^[n] in such a way that for any smooth projective surface X with trivial canonical divisor there is a canonical isomorphism of rings between (H*X)^[n]…

This paper is concerned with the primitive cohomology of a smooth projective hypersurface considered as a linear representation for its automorphism group. Using the Lefschetz-Riemann-Roch formula, the character of this representation is…

A convex projective surface is the quotient of a properly convex open $\Omega$ of $\mathbb{P}(\R)$ by a discret subgroup $\Gamma$ of $\mathrm{SL}_3(\R)$. We give some caracterisations of the fact that a convex projective surface is of…

In this paper, we study a certain cohomology attached to a smooth function, which arose naturally in Poisson geometry. We explain how this cohomology depends on the function, and we prove that it satisfies both the excision and the…

We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the…

Let $X$ be a semistable curve and $L$ a line bundle whose multidegree is uniform, i.e., in the range between those of the structure sheaf and the dualizing sheaf of $X$. We establish an upper bound for $h^0(X,L)$, which generalizes the…

We show that $|mK_X|$ defines a birational map and has no fixed part for some bounded positive integer $m$ for any $\frac{1}{2}$-lc surface $X$ such that $K_X$ is big and nef. For every positive integer $n\geq 3$, we construct a sequence of…

We study the branched holomorphic projective structures on a compact Riemann surface $X$ with a fixed branching divisor $S\, =\, \sum_{i=1}^d x_i$, where $x_i \,\in\, X$ are distinct points. After defining branched ${\rm SO}(3,{\mathbb…

A general hypersurface $X$ of degree $\leq n$ in projective space contains curves $C$ of any genus $g\geq 0$ and sufficiently large degree depnding on $g$ whose normal and conormal bundles have good postulation or natural cohomology in the…

The aim of this paper is twofold. First of all, we confirm a few basic criteria of the finiteness of real forms of a given smooth complex projective variety, in terms of the Galois cohomology set of the discrete part of the automorphism…

We present counterexamples to Fujita's conjecture in positive characteristics. Precisely, we show that over any algebraically closed field $k$ of characteristic $p>0$ and for any positive integer $m$, there exists a smooth projective…

A smooth scheme $X$ over a field $k$ of positive characteristic is said to be strongly liftable over $W_2(k)$, if $X$ and all prime divisors on $X$ can be lifted simultaneously over $W_2(k)$. In this paper, we give a criterion for that…

We study surfaces in $\R^4$ whose tangent spaces have constant principal angles with respect to a plane. Using a PDE we prove the existence of surfaces with arbitrary constant principal angles. The existence of such surfaces turns out to be…

Using the methods developed in [LQW], math.AG/0009132, we obtain a second set of generators for the cohomology ring of the Hilbert scheme of points on an arbitrary smooth projective surface over the field of complex numbers. These…

Let $X$ be a smooth complex projective variety. Using a construction devised to Gathmann, we present a recursive formula for some of the Gromov-Witten invariants of $X$. We prove that, when $X$ is homogeneous, this formula gives the number…

We show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.

S. Boucksom, J.-P. Demailly, M. Paun and Th. Peternell proved that the cone of mobile curves ME(X) of a projective complex manifold X is dual to the cone generated by classes of effective divisors and conjectured an extension of this…

Given a smooth complex projective surface $S$ and an ample divisor $H$ on $S$, consider the blow up of $S$ along $k$ points in general position. Let $H'$ be the pullback of $H$ and $E_1,..., E_k$ be the exceptional divisors. We show that $L…

Let $X$ be a cubic fourfold in $P^5_{C}$. We prove that, assuming the Hodge conjecture for the product $S \times S$, where $S$ is a complex surface, and the finite dimensionality of the Chow motive $h(S)$, there are at most a countable…

Let $X\subset \mathbb P^N$ be a scroll over a smooth curve $C$ and let $\L=\mathcal O_{\mathbb P^N}(1)|_X$ denote the hyperplane bundle. The special geometry of $X$ implies that some sheaves related to the principal part bundles of $\L$ are…