Exceptional collections for mirrors of invertible polynomials
نویسندگان
چکیده
Abstract We prove the existence of a full exceptional collection for derived category equivariant matrix factorizations an invertible polynomial with its maximal symmetry group. This proves conjecture Hirano–Ouchi. In Gorenstein case, we also stronger version this due to Takahashi. Namely, that is strong.
منابع مشابه
Monodromy of Dual Invertible Polynomials
A generalization of Arnold’s strange duality to invertible polynomials in three variables by the first author and A. Takahashi includes the following relation. For some invertible polynomials f the Saito dual of the reduced monodromy zeta function of f coincides with a formal “root” of the reduced monodromy zeta function of its Berglund– Hübsch transpose f . Here we give a geometric interpretat...
متن کاملDibaryons from Exceptional Collections
We discuss aspects of the dictionary between brane configurations in del Pezzo geometries and dibaryons in the dual superconformal quiver gauge theories. The basis of fractional branes defining the quiver theory at the singularity has a K-theoretic dual exceptional collection of bundles which can be used to read off the spectrum of dibaryons in the weakly curved dual geometry. Our prescription ...
متن کاملExceptional Collections for Grassmannians of Isotropic Lines
We construct a full exceptional collection of vector bundles in the derived category of coherent sheaves on the Grassmannian of isotropic two-dimensional subspaces in a symplectic vector space of dimension 2n for all n.
متن کاملExamples for Exceptional Sequences of Invertible Sheaves on Rational Surfaces
The purpose of this note is to give a survey on the results of joint work with Lutz Hille [HP08] and to provide some explicit examples. The general problem addressed in [HP08] is to understand the derived category of coherent sheaves on an algebraic variety (for an introduction and overview on derived categories over algebraic varieties we refer to [Huy06]; see also [Bri06]). An important appro...
متن کاملOrbifold Euler Characteristics for Dual Invertible Polynomials
To construct mirror symmetric Landau–Ginzburg models, P. Berglund, T. Hübsch and M. Henningson considered a pair (f, G) consisting of an invertible polynomial f and an abelian group G of its symmetries together with a dual pair (f̃ , G̃). Here we study the reduced orbifold Euler characteristics of the Milnor fibers of f and f̃ with the actions of the groups G and G̃ respectively and show that they ...
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: Mathematische Zeitschrift
سال: 2023
ISSN: ['1432-1823', '0025-5874']
DOI: https://doi.org/10.1007/s00209-023-03258-x