اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPoisson-de Rham homology of hypertoric varieties and nilpotent cones
461
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove a conjecture of Etingof and the second author for hypertoric varieties, that the Poisson-de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that this conjecture holds for an arbitrary conical variety admitting a symplectic resolution if and only if it holds in degree zero for all normal slices to symplectic leaves. The Poisson-de Rham homology of a Poisson cone inherits a second grading. In the hypertoric case, we compute the resulting 2-variable Poisson-de Rham-Poincare polynomial, and prove that it is equal to a specialization of an enrichment of the Tutte polynomial of a matroid that was introduced by Denham. We also compute this polynomial for S3-varieties of type A in terms of Kostka polynomials, modulo a previous conjecture of the first author, and we give a conjectural answer for nilpotent cones in arbitrary type, which we prove in rank less than or equal to 2.
قيم البحث
اقرأ أيضاً
We use the Beilinson $t$-structure on filtered complexes and the Hochschild-Kostant-Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme $X$ with graded pieces given by the Hodge-completion of t
he derived de Rham cohomology of $X$. Such filtrations have previously been constructed by Loday in characteristic zero and by Bhatt-Morrow-Scholze for $p$-complete negative cyclic and periodic cyclic homology in the quasisyntomic case.
We show that the character variety for a $n$-punctured oriented surface has a natural Poisson structure.
We determine which nilpotent orbits in $E_6$ have normal closure and which do not. We also verify a conjecture about small representations in rings of functions on nilpotent orbit covers for type $E_6$.
Over any smooth algebraic variety over a $p$-adic local field $k$, we construct the de Rham comparison isomorphisms for the etale cohomology with partial compact support of de Rham $mathbb Z_p$-local systems, and show that they are compatible with Po
incare duality and with the canonical morphisms among such cohomology. We deduce these results from their analogues for rigid analytic varieties that are Zariski open in some proper smooth rigid analytic varieties over $k$. In particular, we prove finiteness of etale cohomology with partial compact support of any $mathbb Z_p$-local systems, and establish the Poincare duality for such cohomology after inverting $p$.
Let $mathcal{O}$ be a Richardson nilpotent orbit in a simple Lie algebra $mathfrak{g}$ over $mathbb C$, induced from a Levi subalgebra whose simple roots are orthogonal short roots. The main result of the paper is a description of a minimal set of ge
nerators of the ideal defining $overline{ mathcal{O}}$ in $S mathfrak{g}^*$. In such cases, the ideal is generated by bases of at most two copies of the representation whose highest weight is the dominant short root, along with some fundamental invariants. This extends Broers result for the subregular nilpotent orbit. Along the way we give another proof of Broers result that $overline{ mathcal{O}}$ is normal. We also prove a result connecting a property of invariants related to flat bases to the question of when one copy of the adjoint representation is in the ideal in $S mathfrak{g}^*$ generated by another copy of the adjoint representation and the fundamental invariants.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
