相关论文: Determinant bundle in a family of curves, after A.…

Let $G$ be a reductive group acting on an affine scheme $V$. We study the set of principal $G$-bundles on a smooth projective curve $\mathcal C$ such that the associated $V$-bundle admits a section sending the generic point of $\mathcal C$…

We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces…

We resolve a case of the oriented knot complement conjecture by showing that knots in an orientable circle bundle $N$ over a genus $g \geq 2$ surface $S$ are determined by their complements. We apply this to the setting of canonical knots…

For a domain \Omega in \mathbb{C} and an operator T in \mathcal{B}_n(\Omega), Cowen and Douglas construct a Hermitian holomorphic vector bundle E_T over \Omega corresponding to T. The Hermitian holomorphic vector bundle E_T is obtained as a…

Let C be a smooth complex projective curve of genus at least 2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1. For any k>1, we find two irreducible components of the space of rational…

We give a cohomological classification of vector bundles of rank $2$ on a smooth affine threefold over an algebraically closed field having characteristic unequal to $2$. As a consequence we deduce that cancellation holds for rank $2$…

Let X be a smooth complex projective curve of genus g bigger or equal to 1. If g is bigger than 1 assume further that X is either bielliptic or with general moduli. Under a natural condition on slopes, we prove that there exists a short…

Using Fourier-Mukai transformations, we prove some results about the ring of unipotent vector bundles on elliptic curves in positive characteristics. This ring was determined by Atiyah in characteristic zero, who showed that it is a…

We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a…

We construct connections and characteristic forms for principal bundles over groupoids and stacks in the differentiable, holomorphic and algebraic category using Atiyah sequences associated to transversal tangential distributions.

A theorem of Wiegerinck asserts that the Bergman space of an open subset of the complex numbers is either infinite-dimensional or trivial. Recently, this has been generalized to holomorphic vector bundles over the projective line by the…

We classify all isomorphisms between moduli stacks of vector bundles of fixed determinant on a smooth complex projective of genus at least 4. It is shown that each isomorphism between two different moduli stacks can be described as a…

Let $X$ be a smooth projective curve over an algebraically closed field $k$. Let $\mathcal{G}$ be a parahoric group scheme on $X$ as in \cite{pr}. Via the principle of Hecke correspondences, we set-up relationships between the cohomology of…

In this paper, a notion of a principal $2$-bundle over a Lie groupoid has been introduced. For such principal $2$-bundles, we produced a short exact sequence of VB-groupoids, namely, the Atiyah sequence. Two notions of connection structures…

For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, we prove the existence of a canonical…

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…

Strongly $\mathbb{Z}$-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras $\mathcal{B}(p;q, 0)$ (over a ring of polynomials in one variable) are…

Teichm\"uller curves play an important role in the study of dynamics in polygonal billiards. In this article, we provide a criterion similar to the original M\"oller's criterion, to detect whether a complex curve, embedded in the moduli…

We obtain estimates on the character of the cohomology of an $S^1$-equivariant holomorphic vector bundle over a Kaehler manifold $M$ in terms of the cohomology of the Lerman symplectic cuts and the symplectic reduction of $M$. In…

An abelian category of relative pure motives is constructed along the lines of Andr\'e (over a field of characteristic 0). An algebraic stack is shown to possess a motive in this sense. This motive is studied for the moduli stack of…