اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدClassical sheaf cohomology rings on Grassmannians
76
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let the vector bundle $mathcal{E}$ be a deformation of the tangent bundle over the Grassmannian $G(k,n)$. We compute the ring structure of sheaf cohomology valued in exterior powers of $mathcal{E}$, also known as the polymology. This is the first part of a project studying the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle, a generalization of ordinary quantum cohomology rings of Grassmannians. A companion physics paper [arXiv:1512.08586] describes physical aspects of the theory, including a conjecture for the quantum sheaf cohomology ring, and numerous examples.
قيم البحث
اقرأ أيضاً
In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Q
uantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances in supersymmetric localization to compute A/2 correlation functions and check the general result in examples. In this paper we focus on physics derivations and examples; in a companion paper, we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring.
For a class of monadic deformations of the tangent bundles over nef-Fano smooth projective toric varieties, we study the correlators using quantum sheaf cohomology. We prove a summation formula for the correlators, confirming a conjecture by McOrist
and Melnikov in physics literature. This generalizes the Szenes-Vergne proof of Toric Residue Mirror Conjecture for hypersurfaces.
We complement our previous computation of the Chow-Witt rings of classifying spaces of special linear groups by an analogous computation for the general linear groups. This case involves discussion of non-trivial dualities. The computation proceeds a
long the lines of the classical computation of the integral cohomology of ${rm BO}(n)$ with local coefficients, as done by Cadek. The computations of Chow-Witt rings of classifying spaces of ${rm GL}_n$ are then used to compute the Chow-Witt rings of the finite Grassmannians. As before, the formulas are close parallels of the formulas describing integral cohomology rings of real Grassmannians.
Let $n$ be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent Hessenberg variety in $GL(n,{mathbb{C}})/B$ such that its associated graded ring has graded pieces (i.e.
, homogeneous components) isomorphic to rings which are related to the cohomology rings of Hessenberg varieties in $GL(n-1,{mathbb{C}})/B$, showing the inductive nature of these rings. In previous work, the first two authors, together with Abe and Masuda, gave an explicit presentation of these cohomology rings in terms of generators and relations. We introduce a new set of polynomials which are closely related to the relations in the above presentation and obtain a sequence of equivalence relations they satisfy; this allows us to derive our filtration. In addition, we obtain the following three corollaries. First, we give an inductive formula for the Poincare polynomial of these varieties. Second, we give an explicit monomial basis for the cohomology rings of regular nilpotent Hessenberg varieties with respect to the presentation mentioned above. Third, we derive a basis of the set of linear relations satisfied by the images of the Schubert classes in the cohomology rings of regular nilpotent Hessenberg varieties. Finally, our methods and results suggest many directions for future work; in particular, we propose a definition of Hessenberg Schubert polynomials in the context of regular nilpotent Hessenberg varieties, and outline several open questions pertaining to them.
Let $X$ be an integral scheme of finite presentation over a field. Let $q$ be a singular closed point of $X$. We prove that there exists an open subset $V$ of $X$ containing $q$ such that $V$ admits a resolution, that is, there exists a smooth scheme
$widetilde V$ and a proper birational morphism from $widetilde V$ onto $V$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
