Related papers: Semistable Lefschetz Pencils
We introduce a natural correspondence between artinian monomial almost complete intersections in three variables and punctured hexagonal regions. We use this correspondence to investigate the algebras for the presence of the weak Lefschetz…
We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless Poisson pencil in a single dependent variable using a spectral sequence method. As in the KdV case, we obtain that $BH^p_d(\hat{F}, d_1,d_2)$ is isomorphic to…
We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered cohomologies are finite-dimensional and can be associated…
Monod proved that any continuous cohomology of a semisimple Lie group $G$ can be represented by a measurable cocycle on the associated Furstenberg boundary, which we upgraded to an alternating cocycle. In the current paper we improve that…
We show that isotopy classes of simple closed curves in any oriented surface admit a quandle structure with operations induced by Dehn twists, the Dehn quandle of the surface. We further show that the monodromy of a Lefschetz fibration can…
We prove a Lefschetz duality result for intersection homology. Usually, this result applies to pseudomanifolds with boundary which are assumed to have a "collared neighborhood of their boundary". Our duality does not need this assumption…
We prove the finiteness of the cohomology of torsion-free lattices in a semisimple Lie group of real rank one with coefficients in the distribution vector globalization of Harish-Chandra modules. The cohomology is expressed in terms of…
In this paper we study the Lefschetz properties of monomial complete intersections in positive characteristic. We give a complete classification of the strong Lefschetz property when the number of variables is at least three, which proves a…
Quantum Lefschetz theorem by Coates and Givental gives a relationship between the genus 0 Gromov-Witten theory of X and the twisted theory by a line bundle L on X. We prove the convergence of the twisted theory under the assumption that the…
We introduce two 2-categories which categorify the monodromic Hecke algebra. The first is algebraic in nature and generalizes Abe's theory of Soergel bimodules. The second is a diagrammatic category defined via generators and relations…
The goal of this paper is to generalize a theorem of Fujiwara (formerly Deligne's conjecture) to the situation appearing in a joint work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our…
For a symplectic manifold $(M,\omega)$, not necessarily hard Lefschetz, we prove a version of the Merkulov $d\delta$--lemma. We also study the $d\delta$--lemma and related cohomologies for compact symplectic solvmanifolds.
In this paper, we prove that Gorenstein projective conjecture is left and right symmetric and the co-homology vanishing condition can not be reduced in general. Moreover, the Gorenstein projective conjecture is proved to be true for…
The purpose of this note is to explain a combinatorial description of closed smooth oriented 4-manifolds in terms of positive Dehn twist factorizations of surface mapping classes, and further explore these connections. This is obtained via…
In this paper, we investigate the semistability of logarithmic de Rham sheaves on a smooth projective variety, under suitable conditions. In particular when the Picard number is one, we obtain results for any log Del Pezzo surface, log Fano…
The monodromy conjecture is a mysterious open problem in singularity theory. Its original version relates arithmetic and topological/geometric properties of a multivariate polynomial $f$ over the integers, more precisely, poles of the…
In this paper we give a new proof of the Quantum Unique Ergodicity conjecture for holomorphic integral weight modular forms on the upper half plane. The proof requires only partial results towards the Ramanujan conjecture and the shifted…
In this paper, we prove the integrality conjecture for quotient stacks arising from weakly symmetric representations of reductive groups. Our main result is a decomposition of the cohomology of the stack into finite-dimensional components…
We summarize some results obtained on the problem of gauging the Wess--Zumino term of a d-dimensional bosonic sigma-model. We show that gauged WZ-like terms are in one-to-one correspondence with equivariant cocycles of the target space. By…
Let $R=\mathbb K[x,y,z]$ be a standard graded polynomial ring where $\mathbb K$ is an algebraically closed field of characteristic zero. Let $M = \oplus_j M_j$ be a finite length graded $R$-module. We say that $M$ has the Weak Lefschetz…