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Stability conditions for 3-fold flops

Banff International Research Station for Mathematical Innovation and Discovery

For a 3-fold flopping contraction from X to the spectrum Spec(R) of a complete local Gorenstein ring (R,m) with terminal singularity at m, we give a description of a distinguished connected component of the (normalized) space of Bridgeland stability conditions on certain triangulated categories associated to the flopping contraction. More precisely, we show that the connected component is a regular covering space of the complement of the complexification of a hyperplane arrangement associated to the 3-fold flop. We also determine the autoequivalence groups of the triangulated categories. As an application of these results, we determine the Stringy K Ì ahler Moduli Space (SKMS) for all smooth irreducible 3-fold flops. This is a joint work with Michael Wemyss.

Mathematics; Associative rings and algebras; Algebraic geometry; Representation theory

video/mp4

Author affiliation: Kyoto University

2021-01-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/77138

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/