SEMISTABILITY, MODULAR LATTICES, AND ITERATED LOGARITHMS

F. Haiden; L. Katzarkov; M. Kontsevich; P. Pandit

doi:10.4310/JDG/1679503804

SEMISTABILITY, MODULAR LATTICES, AND ITERATED LOGARITHMS

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

University of Oxford
University of Vienna
National Research University Higher School of Economics
BAS
Institut des Hautes Études Scientifiques
International Centre for Theoretical Sciences

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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.

Originalsprog	Engelsk
Tidsskrift	Journal of Differential Geometry
Vol/bind	123
Udgave nummer	1
Sider (fra-til)	21-66
Antal sider	46
ISSN	0022-040X
DOI	https://doi.org/10.4310/JDG/1679503804
Status	Udgivet - 1. jan. 2023
Udgivet eksternt	Ja

Bibliografisk note

Publisher Copyright:
© 2023 International Press of Boston, Inc.. All rights reserved.

Finansiering

ful discussions. We also thank anonymous referees for carefully proofreading the text and providing suggestions to help improve the exposition. The authors were supported by a Simons research grant, NSF DMS 150908, ERC Gemis, DMS-1265230, DMS-1201475 OISE-1242272 PASI, Simons collaborative Grant - HMS, HSE Megagrant, Laboratory of Mirror Symmetry NRU HSE, RF government grant, ag. 14.641.31.000, Simons Principle Investigator Grant, CKGA VIHREN grant КП-06-ПВ/16. Much of the research was conducted while the authors enjoyed the hospitality of the IHES, the IMSA Miami, and the Laboratory of Mirror Symmetry HSE Moscow

Dokumenter og links

10.4310/JDG/1679503804

SDU link

Tjek adgangen til materialet i Syddansk Universitetsbiblioteks søgemaskine

Citationsformater

@article{c01b232689e3408a9f2930f11d4326de,

title = "SEMISTABILITY, MODULAR LATTICES, AND ITERATED LOGARITHMS",

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.",

author = "F. Haiden and L. Katzarkov and M. Kontsevich and P. Pandit",

year = "2023",

month = jan,

day = "1",

doi = "10.4310/JDG/1679503804",

language = "English",

volume = "123",

pages = "21--66",

journal = "Journal of Differential Geometry",

issn = "0022-040X",

publisher = "International Press of Boston, Inc.",

number = "1",

}

TY - JOUR

T1 - SEMISTABILITY, MODULAR LATTICES, AND ITERATED LOGARITHMS

AU - Haiden, F.

AU - Katzarkov, L.

AU - Kontsevich, M.

AU - Pandit, P.

PY - 2023/1/1

Y1 - 2023/1/1

N2 - 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.

AB - 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.

U2 - 10.4310/JDG/1679503804

DO - 10.4310/JDG/1679503804

M3 - Journal article

AN - SCOPUS:85153381920

SN - 0022-040X

VL - 123

SP - 21

EP - 66

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 1

ER -

SEMISTABILITY, MODULAR LATTICES, AND ITERATED LOGARITHMS

Abstract

Bibliografisk note

Finansiering

Dokumenter og links

SDU link

Fingeraftryk

Citationsformater