Triangulated Categories of Matrix Factorizations for Regular Systems of Weights with Ε = − 1
نویسندگان
چکیده
Abstract. We construct a full strongly exceptional collection in the triangulated category of graded matrix factorizations of a polynomial associated to a non-degenerate regular system of weights whose smallest exponents are equal to −1. In the associated Grothendieck group, the strongly exceptional collection defines a root basis of a generalized root system of sign (l, 0, 2) and a Coxeter element of finite order, whose primitive eigenvector is a regular element in the expanded symmetric domain of type IV with respect to the Weyl group.
منابع مشابه
Matrix Factorizations and Representations of Quivers I
This paper introduces a mathematical definition of the category of D-branes in Landau-Ginzburg orbifolds in terms of A∞-categories. Our categories coincide with the categories of (gradable) matrix factorizations for quasi-homogeneous polynomials. After setting up the necessary definitions, we prove that our category for the polynomial x is equivalent to the derived category of representations o...
متن کاملWeighted Projective Lines Associated to Regular Systems of Weights of Dual Type
We associate to a regular system of weights a weighted projective line over an algebraically closed field of characteristic zero in two different ways. One is defined as a quotient stack via a hypersurface singularity for a regular system of weights and the other is defined via the signature of the same regular system of weights. The main result in this paper is that if a regular system of weig...
متن کاملOrlov’s Equivalence and Tensor Products: from Sheaves to Matrix Factorizations and Back
A special case of a theorem due to Orlov states that for a hypersurface X ⊂ Pn−1 of degree n given by the equation W = 0, there exists an equivalence between the bounded derived category D(cohX) of coherent sheaves on X and the homotopy category HMF(W ) of graded matrix factorizations. We first give a description of this result, and present some methods for doing calculations with it. In the la...
متن کاملWZ factorization via Abay-Broyden-Spedicato algorithms
Classes of Abaffy-Broyden-Spedicato (ABS) methods have been introduced for solving linear systems of equations. The algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes. Here, we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW factorizations of a nonsingular matrix as well as...
متن کاملMatrix Factorizations and Representations of Quivers Ii : Type Ade Case
We study a triangulated category of graded matrix factorizations for a polynomial of type ADE. We show that it is equivalent to the derived category of finitely generated modules over the path algebra of the corresponding Dynkin quiver. Also, we discuss a special stability condition for the triangulated category in the sense of T. Bridgeland, which is naturally defined by the grading.
متن کامل