Okounkov bodies and toric degenerations

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Chebyshev transforms on Okounkov bodies

LetL be a big holomorphic line bundle on a compact complex manifoldX.We show how to associate a convex function on the Okounkov body ofL to any continuous metric e−ψ on L.We will call this the Chebyshev transform of ψ, denoted by c[ψ]. Our main theorem states that the integral of the difference of the Chebyshev transforms of two weights is equal to the relative energy of the weights, which is a...

متن کامل

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 کامل

Toric 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 کامل

Toric 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 کامل

Mixed Toric Residues and Tropical Degenerations

This paper is a follow-up to our paper [19], where we prove a conjecture of Batyrev and Materov, the Toric Residue Mirror Conjecture (TRMC). Here we extend our results, and show that they imply a generalization of this conjecture, the Mixed Toric Residue Mirror Conjecture (MTRMC), which is also due to Batyrev and Materov [3]. Roughly, these conjectures state that the generating function of cert...

متن کامل

ذخیره 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: Mathematische Annalen

سال: 2012

ISSN: 0025-5831,1432-1807

DOI: 10.1007/s00208-012-0880-3