Related papers: Lelong numbers and vector bundles

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 show that on a generic curve, a bundle obtained by successive extensions is stable. We compute the dimension of the set of such extensions. We use degeneration methods specializing the curve to a chain of elliptic components

We study the moduli stacks of real vector bundles of fixed rank and degree on a type I real algebraic curve and determine its mod 2 cohomology algebra in terms of characteristic classes.

We present 25 open questions about moduli spaces of vector bundles and related topics and discuss some longstanding conjectures. We hope to inspire young researchers to engage in this area of research.

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have…

The purpose of this paper is to establish an injectivity theorem generalized to pseudo-effective line bundles with transcendental (non-algebraic) singular hermitian metrics and multiplier ideal sheaves. As an application, we obtain a Nadel…

In this paper, we study the uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials.

We count invariants of the moduli spaces of twisted Higgs bundles on a smooth projective curve.

Consider $E$ a vector bundle over a smooth curve $C$. We compute the $\delta$-invariant of all ample ($\mathbb{Q}$-) line bundles on $\mathbb{P}(E)$ when $E$ is strictly Mumford semistable. We also investigate the case when one assumes that…

We generalize Bertram's work on rank two vector bundles to an irreducible projective nodal curve C. We use extensions of a line bundle L by O_C and the associated `forgetful' map to study a compactification of the moduli space of…

In this note, we present a relationship between Lelong numbers and complex singularity exponents. As an application, we obtain a new proof of Siu's semicontinuity theorem for Lelong numbers.

For a vector bundle V over a curve X of rank n and for each integer r in the range 1 \le r \le n-1, the Segre invariant s_r is defined by generalizing the minimal self-intersection number of the sections on a ruled surface. In this paper we…

We consider spacetime metrics with a given (but quite generic) dependence on a dimensionful parameter such that in the 0 and infinity limits of that parameter the metric becomes singular. We study the isometry groups of the original…

We give an asymptotic formula for the number of $\mathbb{F}_{q}$-rational points over a fixed determinant moduli space of stable vector bundles of rank $r$ and degree $d$ over a smooth, projective curve $X$ of genus $g \geq 2$ defined over…

We desribe vector bundles over a class of noncommutative curves, namely, over noncommutative nodal curves of string type and of almost string type. We also prove that in other cases the classification of vector bundles over a noncommutative…

This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…

We construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.

In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.

We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.