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arXiv · 1706.01073

Semistability, modular lattices, and iterated logarithms

Fabian Haiden·Ludmil Katzarkov·Maxim Kontsevich·Pranav Pandit
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Abstract

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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Fabian Haiden, Ludmil Katzarkov, Maxim Kontsevich, Pranav Pandit. 2017-06-04. Semistability, modular lattices, and iterated logarithms. https://doi.org/10.4310/jdg/1679503804

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