Related papers: Logarithmic co-Higgs bundles
In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,\theta)$, where $G$ is a reductive algebraic group and $\theta$ is an involution of $G$. This generalization involves the notion of a…
We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.
We consider generalized complete intersection manifolds in the product space of projective spaces, and work out useful aspects pertaining to the cohomology of sheaves over them. First, we present and prove a vanishing theorem on the…
The main purpose of this paper is to define the {\it net logarithmic tangent sheaf}, as a generalization of the logarithmic tangent sheaf introduced by P.~Deligne, over the field of complex numbers, and prove some basic properties and give…
We provide notions of numerical effectiveness and numerical flatness for Higgs vector bundles on compact K\"ahler manifolds in terms of fibre metrics. We prove several properties of bundles satisfying such conditions and in particular we…
Winkelmann considered compact complex manifolds $X$ equipped with a reduced effective normal crossing divisor $D\, \subset\, X$ such that the logarithmic tangent bundle $TX(-\log D)$ is holomorphically trivial. He characterized them as…
In previous papers we introduced the notion of special Bohr - Sommerfeld lagrangian cycles on a compact simply connected symplectic manifold with integer symplectic form, and presented the main interesting case: compact simply connected…
The logarithmic connections studied in the paper are direct images of regular connections on line bundles over genus-2 double covers of the elliptic curve. We give an explicit parametrization of all such connections, determine their…
We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as $\mathbb P^3$ or the quintic threefold. We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth…
We study moduli spaces of Higgs bundles with two poles on an elliptic curve. We describe all singular fibers of the Hitchin map, including the nilpotent cone. To achieve this, we consider a modular map that lifts Higgs bundles with five…
In this paper we build bridges between moduli theory of sheaf stable pairs on one hand and birational geometry on the other hand. We will in particular treat moduli of sheaf stable pairs on smooth projective curves in detail and present…
We show that any complex manifold that has a divisor whose normalization has non-zero first Betti number either has a non-trivial holomorphic gerbe which does not trivialize meromorphicly or a meromorphic line bundle not equivalent to any…
Given a compact hyperkaehler manifold $M$ and a holomorphic bundle B over $M$, we consider a Hermitian connection $\nabla$ on B which is compatible with all complex structures on $M$ induced by the hyperkaehler structure. Such a connection…
In math.RT/0201073 we constructed an equivalence between the derived category of equivariant coherent sheaves on the cotangent bundle to the flag variety of a simple algebraic group and a (quotient of) the category of constructible sheaves…
A conic fibration has an associated sheaf of even Clifford algebras on the base. In this paper, we study the relation between the moduli spaces of modules over the sheaf of even Clifford algebras and the Prym variety associated to the conic…
The Corlette-Donaldson-Hitchin-Simpson's correspondence states that, on a compact K\"ahler manifold $(X, \omega )$, there is a one-to-one correspondence between the moduli space of semisimple flat complex vector bundles and the moduli space…
Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups H^1(M,G). On the other hand, if M=\Sigma is a closed Riemann surface, there is a correspondence between holomorphic principal…
In this article, a logahoric Higgs torsor is defined as a parahoric torsor with a logarithmic Higgs field. For a connected complex reductive group $G$, we introduce a notion of stability for logahoric $\mathcal{G}_{\boldsymbol\theta}$-Higgs…
We construct a proper moduli space which is a Deligne-Mumford stack parametrising quasimaps relative to a simple normal crossings divisor in any genus using logarithmic geometry. We show this moduli space admits a virtual fundamental class…
The paper is concerned with cohomology of the small quantum group at a root of unity, and of its upper triangular subalgebra, with coefficients in a tilting module. We relate it to a certain t-structure on the derived category of…