Related papers: Vanishing theorems for parabolic Higgs bundles
For a compact Lie group G we define a regularized version of the Dolbeault cohomology of a G-equivariant holomorphic vector bundles over non-compact Kahler manifolds. The new cohomology is infinite-dimensional, but as a representation of G…
We give a proof of the Kodaira vanishing theorem on smooth complex surfaces using geometric stability conditions. Likewise, we give a new proof of a result of Xie characterizing the counterexamples of the Kodaira vanishing theorem in…
Chow's Theorem and GAGA are renowned results demonstrating the algebraic nature of projective manifolds and, more broadly, projective analytic varieties. However, determining if a particular manifold is projective is not, generally, a…
In this paper, we establish several results related to vanishing theorems for Mather-Jacobian multiplier ideals on a Gorenstein projective variety, including an injectivity theorem, a Nadel-type vanishing theorem, a Griffith-type vanishing…
A Lie algebroid is a generalization of Lie algebra that provides a general framework to describe the symmetries of a manifold. In this paper, we generalize the Kodaira vanishing theorem, which is a basic result in complex geometry, to…
We associate to a pair $(X,D)$, consisting of a smooth scheme with a divisor $D\in \text{Div}(X)\otimes \mathbb{Q}$ whose support is a divisor with normal crossings, a canonical Deligne--Mumford stack over $X$ on which $D$ becomes integral.…
Consider the holomorphic bundle with connection on $\mathbb P^1-\{0,1,\infty\}$ corresponding to the regular hypergeometric differential operator \[ \prod_{j=1}^h(D-\alpha_j)-z\prod_{j=1}^h(D-\beta_j), \qquad D=z\frac{d}{dz}. \] If the…
We prove a surjectivity theorem for the Deligne canonical extension of a polarizable variation of Hodge structure with quasi-unipotent monodromy at infinity along the lines of Esnault-Viehweg. We deduce from it several injectivity theorems…
We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic vector bundles and define positivity in view of $L^2$-estimates. Associated with a suitably positive s.h.m. there is a (coherent) sheaf 0-th kernel of a certain…
Bott vanishing is a strong vanishing result for the cohomology of exterior powers of the cotangent bundle twisted by ample line bundles. Buch-Thomsen-Lauritzen-Mehta conjectured that partial flag varieties (which are not products of…
Using certain Thom spectra appearing in the study of cobordism categories, we show that the odd half of the Miller-Morita-Mumford classes on the mappping class group of a surface with negative Euler characteristic vanish in integral…
We study restriction of logarithmic Higgs bundles to the boundary divisor and we construct the corresponding nearby-cycles functor in positive characteristic. As applications we prove some strong semipositivity theorems for analogs of…
Let M be a compact locally conformal hyperkaehler manifold. We prove a version of Kodaira-Nakano vanishing theorem for M. This is used to show that M admits no holomorphic differential forms, and the cohomology of the structure sheaf…
In this paper, we will provide an alternative definition for the singular Hermitian metric on a vector bundle. Moreover, we discuss the Griffiths and Nakano positivities under this circumstance and prove a generalised Griffiths' vanishing…
We reprove Saito's vanishing theorem for mixed Hodge modules by the method of Esnault and Viehweg. The main idea is to exploit the strictness of direct images on certain branched coverings.
This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in…
The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the signature of the associated hermitian form. In this article, this theorem is generalized to…
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 prove an analog of the Verlinde formula on the moduli space of semistable meromorphic G-Higgs bundles over a smooth curve for a reductive group G whose fundamental group is free. The formula expresses the graded dimension of the space of…
We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the…