Related papers: On vanishing theorems for analytic spaces

Using inversion of adjunction, we deduce from Nadel's theorem a vanishing property for ideals sheaves on projective varieties, a special case of which recovers a result due to Bertram--Ein--Lazarsfeld. This enables us to generalize to a…

We propose a new formulation of a vanishing theorem for surfaces. Although this vanishing theorem follows easily from the well-known Kawamata--Viehweg vanishing theorem, it turns out to be remarkably useful. In particular, it is sufficient…

For proper surjective holomorphic maps from K"ahler manifolds to analytic spaces, we give a decomposition theorem for the cohomology groups of the canonical bundle twisted by Nakano semi-positive vector bundles by means of the higher direct…

We show the vanishing of higher extension groups and torsion groups between linearisation of additive functors from a semi-additive category satisfying some conditions to a category of vector spaces. In particular, we apply our results to…

We formulate and establish a generalization of Koll\'ar's injectivity theorem for adjoint bundles twisted by suitable multiplier ideal sheaves. As applications, we generalize Koll\'ar's torsion-freeness, Koll\'ar's vanishing theorem, and a…

In this note we show a Kawamata-Viehweg vanishing theorem for pl-contractions on threefolds in characteristic $p>5$. We deduce several applications for klt threefolds: the vanishing of higher direct images of structure sheaves of Mori fibre…

In this paper, local monomialization theorems are proven for analytic morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of…

Let $f:X\rightarrow Y$ be a K\"{a}hler fibration from a complex manifold $X$ to an analytic space $Y$. We show several relative Nadel-type vanishing theorems.

A hypothesis of general relativity is that spacetime torsion vanishes identically. This assumption has no empirical support; in fact, a nonvanishing torsion is compatible with all the experimental tests of general relativity. The first part…

On a compact K\"{a}hler manifold $X$ with a holomorphic 2-form $\a$, there is an almost complex structure associated with $\a$. We show how this implies vanishing theorems for the Gromov-Witten invariants of $X$. This extends the approach,…

We prove a rigid analytic analogue of the Artin vanishing theorem. Precisely, we prove (under mild hypotheses) that the geometric etale cohomology of any Zariski-constructible sheaf on any affinoid rigid space $X$ vanishes in all degrees…

We show that, under the definiteness of holomorphic sectional curvature, the spaces of some holomorphic tensor fields on compact Chern-K\"{a}hler-like Hermitian manifolds are trivial. These can be viewed as counterparts to Bochner's…

We prove a general vanishing theorem for the cohomology of products of symmetric and skew-symmetric powers of an ample vector bundle on a smooth complex projective variety. Special cases include an extension of classical theorems of…

We discuss the minimal model program for projective morphisms of complex analytic spaces. Roughly speaking, we show that the results obtained by Birkar--Cascini--Hacon--M\textsuperscript{c}Kernan hold true for projective morphisms between…

We consider compactifications of the space of triples of distinct points in projective $n$-space. One such space is a singular variety of configurations of points and lines; another is the smooth compactification of Fulton and MacPherson;…

We generalize Koll\'ar's package (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to polystable locally abelian parabolic Higgs bundles twisted by a multiplier ideal sheaf associated with an…

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that…

We prove the vanishing of bounded cohomology with separable dual coefficients for many groups of interest in geometry, dynamics, and algebra. These include compactly supported structure-preserving diffeomorphism groups of certain manifolds;…

We study the minimal model program for lc pairs on projective morphism between complex analytic spaces. More precisely, we generalize the results by Birkar and the second author to the setup by Fujino.

This paper contains some vanishing theorems for $L^2$ harmonic forms on complete Riemannian manifolds with a weighted Poincar\'e inequality and a certain lower bound of the curvature. The results are in the spirit of Li-Wang and Lam, but…