相关论文: Convex Fujita numbers: projective bundles

We establish a structure result for the universal abelian variety over the moduli space A_5, in terms of discriminant curves of conic bundles over a del Pezzo surface. In particular, this gives a very simple unirational parametrization of…

We prove that the multiplication of sections of globally generated line bundles on a model wonderful variety M of simply connected type is always surjective. This follows by a general argument which works for every wonderful variety and…

This paper generalises Mori's famous theorem about "Projective manifolds with ample tangent bundles" to normal projective varieties in the following way: A normal projective variety over $\mathbb{C}$ with ample tangent sheaf is isomorphic…

We classify smooth projective surfaces that are quotients of abelian surfaces by finite groups.

We study the splitting properties of the Verlinde bundles over elliptic curves. Our methods rely on the explicit description of the moduli space of semistable vector bundles on elliptic curves, and on the analysis of the symmetric powers of…

Let $X$ be a projective variety over a field. In this paper, we will construct a moduli space of very ample line bundles on $X$. In doing so, we develop a generalization of Fitting ideals to complexes of sheaves on $X$. We give other…

Given a complex projective surface with an ADE singularity and p_{g}=0, we construct ADE bundles over it and its minimal resolution. Furthermore, we descibe their minuscule representation bundles in terms of configurations of (reducible)…

Bolibruch's examples of representations of pi_1(P^1-finitely many points) which are not realizable by Fuchsian differential systems are adapted to curves of higher genus.

We study quotients of multi-graded bundles, including double vector bundles. Among other things, we show that any such quotient fits into a tower of affine bundles. Applications of the theory include a construction of normal bundles for…

We discuss the Morse estimates for the curvature of several metrics on Semple weighted projective bundle over a projective variety. Following Demailly works on holomorphic Morse inequalities we show an analogue of his results along the…

Let $X$ be an abelian variety defined over an algebraically closed field $k$. We consider theta groups associated to \emph{simple semi-homogenous vector bundles of separable type} on $X$. We determine the structure and representation theory…

We construct symplectic surface bundles over surfaces with positive signatures for all but 18 possible pairs of fiber and base genera. Meanwhile, we determine the commutator lengths of a few new mapping classes.

After recalling the basic notions concerning Higgs-Grassmannian schemes, I review how these latter can be used to define generalisations of the notion of positivity conditions, such as numerically flatness, which "feel" the Higgs field.…

We study global deformations of certain projective bundles over projective spaces. We show that any projective global deformation of a projective bundle over $\bP^1$ carries the structure of a projective bundle over some projective space.…

We examine \'etale covers of genus two curves that occur in the linear system of a polarizing line bundle of type $(1,d)$ on a complex abelian surface. We give results counting fixed points of involutions on such curves as well as…

We study the logarithmic vector bundles associated to arrangements of smooth irreducible curves with small degree on the blow-up of the projective plane at one point. We then investigate whether they are Torelli arrangements, that is, they…

Among recently introduced new notions in real algebraic geometry is that of regulous functions. Such functions form a foundation for the development of regulous geometry. Several interesting results on regulous varieties and regulous…

Given a complex curve C of genus 2, there is a well-known relationship between the moduli space of rank 3 semistable bundles on C and a cubic hypersurface known as the Coble cubic. Some of the aspects of this is known to be related to the…

It is known that a vector bundle E on a smooth projective curve Y defined over an algebraically closed field is semistable if and only if there is a vector bundle F on Y such that the cohomologies of E\otimes F vanish. We extend this…

We determine some classes of varieties X - that include the varieties with numerically effective tangent bundle - satisfying the following property: if E is a Higgs bundle such that f*E is semistable for any morphism f from a smooth…