Related papers: Convex Fujita numbers: projective bundles

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…

Motivated by the problem of finding algebraic constructions of finite coverings in commutative algebra, the Steinitz realization problem in number theory, and the study of Hurwitz spaces in algebraic geometry, we investigate the vector…

Let $Y \to B$ be a relative smooth projective curve over an affine integral base scheme $B$ of positive characteristic. We provide for all prime characteristics example classes of vector bundles $\mathcal{S}$ over $Y$ such that…

We prove that moduli spaces of semistable vector bundles of coprime rank and degree over a non-singular real projective curve are maximal real algebraic varieties if and only if the base curve itself is maximal. This provides a new family…

In this paper we study the positivity of the cotangent bundle of projective manifolds. We conjecture that the cotangent bundle is pseudoeffective if and only the manifold has non-zero symmetric differentials. We confirm this conjecture for…

Let $X$ be a smooth projective variety over an algebraically closed field $\mathbb{K}$ with arbitrary characteristic. Suppose $L$ is an ample and globally generated line bundle. By Castelnuovo--Mumford regularity, we show that $K_X \otimes…

We prove a semistable reduction theorem for principal bundles on curves in almost arbitrary characteristics. For exceptional groups we need some small explicit restrictions on the characteristic.

We study Brauer-Severi surface bundles over smooth projective varieties via root stacks, with a view towards applications to failure of stable rationality.

Generalizing work done by Miyaoka and others in the case of divisors and of curves, we compute the cones of effective cycles of arbitrary dimension on a projective bundle over a complex projective curve in terms of the numerical data in an…

In this paper we construct the moduli of semistable principal bundles with structure group a semisimple group, over nonsingular curves in positive characteristic, with good bounds on the prime.

We survey results concerning behavior of positivity of line bundles and possible vanishing theorems in positive characteristic. We also try to describe variation of positivity in mixed characteristic. These problems are very much related to…

We explain how to define an embedding of a tame stack over a noetherian ring into a certain generalization of a weighted projective stack using a notion of ample vector bundle on the stack. As applications we construct algebraic moduli…

We generalize a result of Fujita, on the decomposition of Hodge bundles over curves, to the case of a higher dimensional base.

A vector bundle on a smooth projective variety, if it is generically generated by global sections, yields a rational map to a Grassmannian, called Kodaira map. We investigate the asymptotic behaviour of the Kodaira maps for the symmetric…

We use presentations of the Cox rings of projectivized toric vector bundles and elements of matroid theory to compute Newton-Okounkov bodies, effective cones, and nef cones of these spaces. As an application we analyze the Fano property and…

In this work, we investigate the positivity of logarithmic and orbifold cotangent bundles along hyperplane arrangements in projective spaces. We show that a very interesting example given by Noguchi (as early as in 1986) can be pushed…

In this article, the existence of Ulrich bundles on projective bundles $\mathbb P(E) \to X$ is discussed. In the case, that the base variety $X$ is a curve or surface, a close relationship between Ulrich bundles on $X$ and those on $\mathbb…

In this paper we focus on the problem of computing the number of moduli of the so called Severi varieties (denoted by V(|D|, \delta)), which parametrize universal families of irreducible, \delta-nodal curves in a complete linear system |D|,…

We show that a principal G bundle on a smooth projective curve over a finite field is strongly semistable if and only if it is defined by a representation of the fundamental group scheme of the curve into G.

We prove results concerning the specialisation of torsion line bundles on a variety $V$ defined over $\mathbb{Q}$ to ideal classes of number fields. This gives a new general technique for constructing and counting number fields with large…