ترغب بنشر مسار تعليمي؟ اضغط هنا

Some Applications of the Mirror Theorem for Toric Stacks

130   0   0.0 ( 0 )
 نشر من قبل Tom Coates
 تاريخ النشر 2014
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We use the mirror theorem for toric Deligne-Mumford stacks, proved recently by the authors and by Cheong-Ciocan-Fontanine-Kim, to compute genus-zero Gromov-Witten invariants of a number of toric orbifolds and gerbes. We prove a mirror theorem for a class of complete intersections in toric Deligne-Mumford stacks, and use this to compute genus-zero Gromov-Witten invariants of an orbifold hypersurface.



قيم البحث

اقرأ أيضاً

We prove a Givental-style mirror theorem for toric Deligne--Mumford stacks X. This determines the genus-zero Gromov--Witten invariants of X in terms of an explicit hypergeometric function, called the I-function, that takes values in the Chen--Ruan orbifold cohomology of X.
Using the mirror theorem [CCIT15], we give a Landau-Ginzburg mirror description for the big equivariant quantum cohomology of toric Deligne-Mumford stacks. More precisely, we prove that the big equivariant quantum D-module of a toric Deligne-Mumford stack is isomorphic to the Saito structure associated to the mirror Landau-Ginzburg potential. We give a GKZ-style presentation of the quantum D-module, and a combinatorial description of quantum cohomology as a quantum Stanley-Reisner ring. We establish the convergence of the mirror isomorphism and of quantum cohomology in the big and equivariant setting.
204 - Hiroshi Iritani 2019
We introduce a global Landau-Ginzburg model which is mirror to several toric Deligne-Mumford stacks and describe the change of the Gromov-Witten theories under discrepant transformations. We prove a formal decomposition of the quantum cohomology D-mo dules (and of the all-genus Gromov-Witten potentials) under a discrepant toric wall-crossing. In the case of weighted blowups of weak-Fano compact toric stacks along toric centres, we show that an analytic lift of the formal decomposition corresponds, via the $widehat{Gamma}$-integral structure, to an Orlov-type semiorthogonal decomposition of topological $K$-groups. We state a conjectural functoriality of Gromov-Witten theories under discrepant transformations in terms of a Riemann-Hilbert problem.
231 - Hiroshi Iritani 2015
We identify a certain universal Landau-Ginzburg model as a mirror of the big equivariant quantum cohomology of a (not necessarily compact or semipositive) toric manifold. The mirror map and the primitive form are constructed via Seidel elements and s hift operators for equivariant quantum cohomology. Primitive forms in non-equivariant theory are identified up to automorphisms of the mirror.
We use ideas from algebraic geometry and dynamical systems to explain some ways that control points influence the shape of a Bezier curve or patch. In particular, we establish a generalization of Birchs Theorem and use it to deduce sufficient conditi ons on the control points for a patch to be injective. We also explain a way that the control points influence the shape via degenerations to regular control polytopes. The natural objects of this investigation are irrational patches, which are a generalization of Krasauskass toric patches, and include Bezier and tensor product patches as important special cases.
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