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- W2753408536 abstract "Smooth threefold flops with irreducible centres are classified by the length invariant, which takes values 1, 2, 3, 4, 5 or 6. This classification by Katz and Morrison identifies 6 possible partial resolutions of Kleinian singularities that can occur as generic hyperplane sections, and the simultaneous resolutions associated to such a partial resolution produce the universal flop of length $l$. In this paper we translate these ideas into noncommutative algebra. We introduce the universal flopping algebra of length $l$ from which the universal flop of length $l$ can be recovered by a moduli construction, and we present each of these algebras as the path algebra of a quiver with relations. This explicit realisation can then be used to construct examples of NCCRs associated threefold flops of any length as quiver with relations defined by superpotentials, to recover the matrix factorisation description of the universal flop conjectured by Curto and Morrison, and to realise examples of contraction algebras." @default.
- W2753408536 created "2017-09-15" @default.
- W2753408536 creator A5023870543 @default.
- W2753408536 date "2017-09-08" @default.
- W2753408536 modified "2023-09-27" @default.
- W2753408536 title "The length classification of threefold flops via noncommutative algebras" @default.
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