Semistability, modular lattices, and iterated logarithms


Haiden, F
Katzarkov, L
Kontsevich, M
Pandit, P


Journal of Differential Geometry

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We provide a complete description of the asymptotics of the gradient flow on the space of metrics on any semistable quiver representation. This involves a recursive construction of approximate solutions and the appearance of iterated logarithms and a limiting filtration of the representation. The filtration turns out to have an algebraic definition which makes sense in any finite length modular lattice. This is part of a larger project by the authors to study iterated logarithms in the asymptotics of gradient flows, both in finite and infinite dimensional settings.

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Journal Article