Related papers: On the logarithmic connections over curves

Let $X$ be an irreducible smooth complex projective variety. Let $G$ be a linear algebraic group over $\mathbb{C}$. We define the notion of Lie algebroid valued connection on holomorphic principal $G$--bundles on $X$, and study their basic…

We prove that the moduli space of curves with level structures has an enormous amount of rational cohomology in its cohomological dimension. As an application, we prove that the coherent cohomological dimension of the moduli space of curves…

Let $ \mathcal{D} = \{D_{1}, \ldots, D_{\ell}\} $ be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space $ \mathbb{P}^{n} $ and let $ \Omega^{1}_{\mathbb{P}^{n}}(log \mathcal{D}) $ be the logarithmic…

This paper studies the moduli space of stable surfaces of general type. The moduli space component containing the moduli point of a product of smooth curves of general type is proved to be the product of the moduli spaces of the curves,…

Let X be a compact connected Riemann surface equipped with an anti-holomorphic involution \sigma. Let G be a connected complex reductive affine algebraic group, and let \sigma_G be a real form of G. We consider holomorphic principal…

Recently, the authors of this paper introduced logarithmic Hochschild (co)homology of logarithmic spaces in a geometric way using formality of derived intersections. In this paper, the authors extend the decomposition theorem for the…

We study jumping lines loci of logarithmic bundles associated with finite sets of points in the projective plane. Using the interpolation matrix introduced in [DMTG25], we describe these loci as the zero sets of explicit determinants…

A ribbon is a first-order thickening of a non-singular curve. Motivated by a question of Eisenbud and Green, we show that a compactification of the moduli space of line bundles on a ribbon is given by the moduli space of semi-stable…

Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G-bundles on any smooth projective curve over k.

We present closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on several Calabi-Yau threefolds realised as complete intersections in products of projective spaces. The formulae have been obtained by…

We define a moduli space of rational curves with finite-order automorphism and weighted orbits, and we prove that the combinatorics of its boundary strata are encoded by a particular polytopal complex that also captures the algebraic…

We study moduli stacks of principal $\Bbb C^*$-bundles over nodal complex algebraic curves and determine their rational cohomology algebras in terms of Chern classes.

We give an explicit groupoid presentation of certain stacks of vector bundles on formal neighborhoods of rational curves inside algebraic surfaces. The presentation involves a M\"obius type action of an automorphism group on a space of…

In this note we develop a coalgebraic approach to the study of solutions of linear difference equations over modules and rings. Some known results about linearly recursive sequences over base fields are generalized to linearly (bi)recursive…

The aim of this paper is to study some modular contractions of the moduli space of stable pointed curves. These new moduli spaces, which are modular compactifications of the moduli space of smooth pointed curves, are related with the…

In this paper we proof the existence of a linearization for singular principal G-bundles not depending on the base curve. This allow us to construct the relative compact moduli space of {\delta}-(semi)stable singular principal G-bundles…

It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the…

Algebraic parabolic bundles on smooth projective curves over algebraically closed field of positive characteristic is defined. It is shown that the category of algebraic parabolic bundles is equivalent to the category of orbifold bundles…

For $4 \nmid L$ and $g$ large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level $L$ structures. In particular, we determine the divisibility properties of the…

Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…