ﻻ يوجد ملخص باللغة العربية
We prove several results concerning the intersection cohomology and the perverse filtration associated with a Lagrangian fibration of an irreducible symplectic variety. We first show that the perverse numbers only depend on the deformation equivalence class of the ambient variety. Then we compute the border of the perverse diamond, which further yields a complete description of the intersection cohomology of the Lagrangian base and the invariant cohomology classes of the fibers. Lastly, we identify the perverse and Hodge numbers of intersection cohomology when the irreducible symplectic variety admits a symplectic resolution. These results generalize some earlier work by the second and third authors in the nonsingular case.
Let $(M,I, Omega)$ be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration $pi:; M mapsto X$, and $eta$ a closed form of Hodge type (1,1)+(2,0) on $X$. We prove that $Omega:=Omega+pi^* eta$ is again a holomorphically
Let $X^{2n}subseteq mathbb{P} ^N$ be a smooth projective variety. Consider the intersection cohomology complex of the local system $R^{2n-1}pi{_*}mathbb{Q}$, where $pi$ denotes the projection from the universal hyperplane family of $X^{2n}$ to ${(mat
We investigate the equivariant intersection cohomology of a toric variety. Considering the defining fan of the variety as a finite topological space with the subfans being the open sets (that corresponds to the toric topology given by the invariant o
Let $M$ be a hyperkahler manifold of maximal holonomy (that is, an IHS manifold), and let $K$ be its Kahler cone, which is an open, convex subset in the space $H^{1,1}(M, R)$ of real (1,1)-forms. This space is equipped with a canonical bilinear symme
Let $C$ be a smooth projective curve of genus $2$. Following a method by O Grady, we construct a semismall desingularization $tilde{mathcal{M}}_{Dol}^G$ of the moduli space $mathcal{M}_{Dol}^G$ of semistable $G$-Higgs bundles of degree 0 for $G=GL(2,