ترغب بنشر مسار تعليمي؟ اضغط هنا

Explicit models for perverse sheaves

104   0   0.0 ( 0 )
 نشر من قبل Luis Narvaez-Macarro
 تاريخ النشر 2002
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process of gluing $t$-structures and we exhibit explicit abelian categories defined in terms of standard sheaves categories which are equivalent to the former ones. In particular, we are able to realize perverse sheaves categories as non full abelian subcategories of the usual bounded complexes of sheaves categories. Our methods use induction on perversities. In this paper, we restrict ourselves to the two-strata case, but our results extend to the general case.



قيم البحث

اقرأ أيضاً

In algebraic geometry, one often encounters the following problem: given a scheme X, find a proper birational morphism from Y to X where the geometry of Y is nicer than that of X. One version of this problem, first studied by Faltings, requires Y to be Cohen-Macaulay; in this case Y is called a Macaulayfication of X. In another variant, one requires Y to satisfy the Serre condition S_r. In this paper, the authors introduce generalized Serre conditions--these are local cohomology conditions which include S_r and the Cohen-Macaulay condition as special cases. To any generalized Serre condition S_rho, there exists an associated perverse t-structure on the derived category of coherent sheaves on a suitable scheme X. Under appropriate hypotheses, the authors characterize those schemes for which a canonical finite S_rho-ification exists in terms of the intermediate extension functor for the associated perversity. Similar results, including a universal property, are obtained for a more general morphism extension problem called S_rho-extension.
189 - Donu Arapura , Botong Wang 2021
We conjecture that any perverse sheaf on a compact aspherical Kahler manifold has non-negative Euler characteristic. This extends the Singer-Hopf conjecture in the Kahler setting. We verify the stronger conjecture when the manifold X has non-positive holomorphic bisectional curvature. We also show that the conjecture holds when X is projective and in possession of a faithful semi-simple rigid local system. The first result is proved by expressing the Euler characteristic as an intersection number involving the characteristic cycle, and then using the curvature conditions to deduce non-negativity. For the second result, we have that the local system underlies a complex variation of Hodge structure. We then deduce the desired inequality from the curvature properties of the image of the period map.
We introduce moduli spaces of stable perverse coherent systems on small crepant resolutions of Calabi-Yau 3-folds and consider their Donaldson-Thomas type counting invariants. The stability depends on the choice of a component (= a chamber) in the co mplement of finitely many lines (= walls) in the plane. We determine all walls and compute generating functions of invariants for all choices of chambers when the Calabi-Yau is the resolved conifold. For suitable choices of chambers, our invariants are specialized to Donaldson-Thomas, Pandharipande-Thomas and Szendroi invariants.
Another introduction to perverse sheaves with some exercises. Expanded version of five lectures at the 2015 PCMI.
417 - Rina Anno 2016
We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories ${mathcal D}_{2n}$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element of $sl_{2n}$ with two equal Jordan blocks. This representation allows us to enumerate the irreducible objects in the heart of the exotic $t$-structure on ${mathcal D}_{2n}$ by crossingless matchings of $2n$ points on a circle. We also describe the algebra of endomorphisms of the direct sum of the irreducible objects.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا