Matrix factorizations for domestic triangle singularities

• Autorzy: Dawid Edmund Kędzierski , Helmut Lenzing , Hagen Meltzer
• Języki publikacji: EN

Abstrakty

EN

Working over an algebraically closed field k of any characteristic, we determine the matrix factorizations for the-suitably graded-triangle singularities $f = x^{a} + y^{b} + z^{c}$ of domestic type, that is, we assume that (a,b,c) are integers at least two satisfying 1/a + 1/b + 1/c > 1. Using work by Kussin-Lenzing-Meltzer, this is achieved by determining projective covers in the Frobenius category of vector bundles on the weighted projective line of weight type (a,b,c). Equivalently, in a representation-theoretic context, we can work in the mesh category of ℤ Δ̃ over k, where Δ̃ is the extended Dynkin diagram corresponding to the Dynkin diagram Δ = [a,b,c]. Our work is related to, but in methods and results different from, the determination of matrix factorizations for the ℤ-graded simple singularities by Kajiura-Saito-Takahashi. In particular, we obtain symmetric matrix factorizations whose entries are scalar multiples of monomials, with scalars taken from {0,±1}.

Kategorie tematyczne

• 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
• 14J17: Singularities
• 16G60: Representation type (finite, tame, wild, etc.)
• 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 140
• Numer: 2
• Strony: 239-278

Daty

wydano

2015

Twórcy

autor

Dawid Edmund Kędzierski

• Instytut Matematyki, Uniwersytet Szczeciński, 70-451 Szczecin, Poland

autor

Helmut Lenzing

• Institut für Mathematik, Universität Paderborn, 33095 Paderborn, Germany

autor

Hagen Meltzer

• Instytut Matematyki, Uniwersytet Szczeciński, 70451 Szczecin, Poland

Identyfikatory

DOI

10.4064/cm140-2-6