Related papers: Log-terminal singularities and vanishing theorems

We present a new relation between an invariant of singularities in characteristic zero (the log canonical threshold) and an invariant of singularities defined via the Frobenius morphism in positive characteristic (the F-pure threshold). We…

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…

Let (S, B) be the log pair associated with a projective completion of a smooth quasi-projective surface V . Under the assumption that the boundary B is irreducible, we obtain an algorithm to factorize any automorphism of V into a sequence…

We prove a general criterion for the vanishing of second bounded cohomology (with trivial real coefficients) for groups that admit an action satisfying certain mild hypotheses. This leads to new computations of the second bounded cohomology…

Let $k$ be an infinite finitely generated field of characteristic $p>0$. Fix a separated scheme $X$ smooth, geometrically connected, and of finite type over $k$ and a smooth proper morphism $f:Y\rightarrow X$. The main result of this paper…

We correct the proof and slightly strengthen a Kodaira-type vanishing theorem for singular varieties originally due to Jaffe and the first author. Specifically, we show that if $L$ is a nef and big line bundle on a projective variety of…

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 prove that the pull-back of a quasi-log scheme by a smooth quasi-projective morphism has a natural quasi-log structure. We treat an application to log Fano pairs. This paper also contains a proof of the simple connectedness of log Fano…

For a curve C and a reductive group G in prime characteristic, we relate the de Rham moduli of logarithmic G-connections on C to the Dolbeault moduli of logarithmic G-Higgs bundles on the Frobenius twist of C. We name this result the…

Suppose $X$ is a smooth projective scheme of finite type over a field $K$, $\mathcal{E}$ is a locally free ${\mathcal{O}}_{X}$-bimodule of rank 2, $\mathcal{A}$ is the non-commutative symmetric algebra generated by $\mathcal{E}$ and ${\sf…

Let $G$ be a semisimple algebraic group defined over an algebraically closed field of characteristic 0 and $P$ be a parabolic subgroup of $G$. Let $M$ be a $P$-module and $V$ be a $P$-stable closed subvariety of $M$. We show in this paper…

We extend the dimension and strong linearity results of generic vanishing theory to bundles of holomorphic forms and rank one local systems, and more generally to certain coherent sheaves of Hodge-theoretic origin associated to irregular…

We study the singularities of closures of Iwahori orbits on loop spaces of symmetric varieties extending the celebrated work of Lusztig-Vogan to the affine setting. We show that the IC-complexes of orbit closures (with possible non-trivial…

We show that the algebraic local fundamental group of any klt singularity as well as the algebraic fundamental group of the smooth locus of any log Fano variety are finite.

This paper contains two theorems concerning the vanishing of natural transformations of (co)homology functors. Precisely, assume that $R$ is a right noetherian ring and $f: M\rt N$ is a morphism of finitely generated right $R$-modules. The…

Given a normal $\mathbb{Q}$-Gorenstein complex variety $X$, we prove that if one spreads it out to a normal $\mathbb{Q}$-Gorenstein scheme $\mathcal{X}$ of mixed characteristic whose reduction $\mathcal{X}_p$ modulo $p$ has normal $F$-pure…

The goal of this paper is to establish fundamental properties of the Hochschild, topological Hochschild, and topological cyclic homologies of commutative, Noetherian rings, which are assumed only to be F-finite in the majority of our…

Given a quasi-projective variety X with only Kawamata log terminal singularities, we study the obstructions to extending finite \'etale covers from the smooth locus $X_{\mathrm{reg}}$ of $X$ to $X$ itself. A simplified version of our main…

We construct modular resolutions of singularities for splitting loci, and use them to show that tame splitting loci have rational singularities. As a corollary of our results and Hurwitz-Brill-Noether theory, we prove that if $C$ is a…

Let $X$ be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves $R^if_*\Omega^p_{\tilde X}(\log E)$, where $f: \tilde{X} \to X$ is a strong log resolution of singularities with reduced exceptional divisor $E$.…