Toric degenerations of cluster varieties and cluster duality
نویسندگان
چکیده
منابع مشابه
Toric Degenerations of Spherical Varieties
We prove that any affine, resp. polarized projective, spherical variety admits a flat degeneration to an affine, resp. polarized projective, toric variety. Motivated by Mirror Symmetry, we give conditions for the limit toric variety to be a Gorenstein Fano, and provide many examples. We also provide an explanation for the limits as boundary points of the moduli space of stable pairs whose exist...
متن کاملToric Degenerations of Weight Varieties and Applications
We show that a weight variety, which is a quotient of a flag variety by the maximal torus, admits a flat degeneration to a toric variety. In particular, we show that the moduli spaces of spatial polygons degenerate to polarized toric varieties with the moment polytopes defined by the lengths of their diagonals. We extend these results to more general Flaschka-Millson hamiltonians on the quotien...
متن کاملToric Degenerations of Bott-samelson Varieties
We study Bott-Samelson varieties for the group GLn(C), their toric degenerations and standard monomial type bases for their homogeneous coordinate rings. A 3-dimensional example is described in detail.
متن کاملToric Degenerations and Batyrev-borisov Duality
In [5], Bernd Siebert and I introduced the notion of a toric degeneration of CalabiYau varieties. The initial goal is to produce a method of constructing mirror pairs which combines the Strominger-Yau-Zaslow (differential geometric) approach to mirror symmetry and the older Batyrev-Borisov (algebro-geometric) approach to mirror symmetry. Our belief is that in doing so we will produce a new, muc...
متن کاملDegenerations of real irrational toric varieties
A real irrational toric variety X is an analytic subset of the simplex associated to a finite configuration of real vectors. The positive torus acts on X by translation, and we consider limits of sequences of these translations. Our main result identifies all possible Hausdorff limits of translations of X as toric degenerations using elementary methods and the geometry of the secondary fan of t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2020
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x2000740x