Contents
Algebraic and Complex Geometry
A smooth compactification of spaces of stability conditions: the case of the
$A_{n}$-quiver
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- 18 November 2024, e101
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We propose a notion of multi-scale stability conditions with the goal of providing a smooth compactification of the quotient of the space of projectivized Bridgeland stability conditions by the group of autoequivalence. For the case of the 3CY category associated with the
$A_n$-quiver, this goal is achieved by defining a topology and complex structure that relies on a plumbing construction.We compare this compactification to the multi-scale compactification of quadratic differentials and briefly indicate why even for the Kronecker quiver, this notion needs refinement to provide a full compactification.
Algebra
Fusion Systems and Rank
$2$ Simple Groups of Lie Type
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- 15 November 2024, e102
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For any prime p and S a p-group isomorphic to a Sylow p-subgroup of a rank
$2$ simple group of Lie type in characteristic p, we determine all saturated fusion systems supported on S up to isomorphism.
