Mirror Symmetry and Cluster Varieties
نویسنده
چکیده
2 Toric Varieties 7 2.1 Constructing an atlas for a toric variety from a fan . . . . . . . . . . . . . . . . . . . . 7 2.2 Cones correspond to torus orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Maps of fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 The quotient construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 The Dual Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.7 Piecewise Linear Functions and Polytopes . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.8 Projective toric varieties from convex polytopes . . . . . . . . . . . . . . . . . . . . . . 13 2.9 Moment maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.10 Toric degenerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
منابع مشابه
Vertex Algebras and Mirror Symmetry
Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish th...
متن کاملMirror Congruence For Rational Points On Calabi-Yau Varieties
One of the basic problems in arithmetic mirror symmetry is to compare the number of rational points on a mirror pair of Calabi-Yau varieties. At present, no general algebraic geometric definition is known for a mirror pair. But an important class of mirror pairs comes from certain quotient construction. In this paper, we study the congruence relation for the number of rational points on a quoti...
متن کاملSupermanifolds, Rigid Manifolds and Mirror Symmetry
By providing a general correspondence between Landau-Ginzburg orbifolds and nonlinear sigma models, we find that the elusive mirror of a rigid manifold is actually a supermanifold. We also discuss when sigma models with super-target spaces are conformally invariant and describe their chiral rings. Both supermanifolds with and without Kähler moduli are considered. This work leads us to conclude ...
متن کاملMirror Symmetry Constructions: A Review
We review various constructions of mirror symmetry in terms of Landau-Ginzburg orbifolds for arbitrary central charge c and Calabi-Yau hypersurfaces and complete intersections in toric varieties. In particular it is shown how the different techniques are related. To appear in Essays on Mirror Manifolds II
متن کاملHomological Mirror Symmetry for the Genus Two Curve
The Homological Mirror Symmetry conjecture relates symplectic and algebraic geometry through their associated categorical structures. Kontsevich’s original version [31] concerned Calabi-Yau varieties. There, we now have complete proofs of some cases [44, 49] and partial results for many more [32, 24]. Soon after, Kontsevich proposed an analogue of the conjecture for Fano varieties. This was gra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017