Moduli stacks of Serre stable representations in tilting theory
Autor: | Daniel Chan, Boris Lerner |
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Jazyk: | angličtina |
Rok vydání: | 2015 |
Předmět: |
Pure mathematics
Functor General Mathematics 010102 general mathematics Tilting theory 010103 numerical & computational mathematics Algebraic geometry 01 natural sciences Representation theory Moduli 14D23 16G20 Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Stack (abstract data type) FOS: Mathematics Sheaf Abelian category Representation Theory (math.RT) 0101 mathematics Algebraic Geometry (math.AG) Mathematics - Representation Theory Mathematics |
Popis: | We introduce a new moduli stack, called the Serre stable moduli stack, which corresponds to studying families of point objects in an abelian category with a Serre functor. This allows us in particular, to re-interpret the classical derived equivalence between most concealed-canonical algebras and weighted projective lines by showing they are induced by the universal sheaf on the Serre stable moduli stack. We explain why the method works by showing that the Serre stable moduli stack is the tautological moduli problem that allows one to recover certain nice stacks such as weighted projective lines from their moduli of sheaves. As a result, this new stack should be of interest in both representation theory and algebraic geometry. |
Databáze: | OpenAIRE |
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