Bridgeland stability conditions on the acyclic triangular quiver

George Dimitrov; Ludmil Katzarkov

doi:10.1016/j.aim.2015.10.014

Bridgeland stability conditions on the acyclic triangular quiver

George Dimitrov, Ludmil Katzarkov

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Using results in our previous paper "Non-semistable exceptional objects in hereditary categories", we focus here on studying the topology of the space of Bridgeland stability conditions on D^b(Rep_k(Q)), where Q= and k is an algebraically closed field. In particular, we prove that this space is contractible (in the previous paper it was shown that it is connected).

Original language	English (US)
Pages (from-to)	825-886
Number of pages	62
Journal	Advances in Mathematics
Volume	288
DOIs	https://doi.org/10.1016/j.aim.2015.10.014
State	Published - Jan 22 2016

Keywords

Affine quiver
Bridgeland stability conditions on triangulated categories
Contractible space
Exceptional collections
Tame representation type quiver

ASJC Scopus subject areas

Mathematics(all)

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10.1016/j.aim.2015.10.014

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title = "Bridgeland stability conditions on the acyclic triangular quiver",

abstract = "Using results in our previous paper {"}Non-semistable exceptional objects in hereditary categories{"}, we focus here on studying the topology of the space of Bridgeland stability conditions on Db(Repk(Q)), where Q= and k is an algebraically closed field. In particular, we prove that this space is contractible (in the previous paper it was shown that it is connected).",

keywords = "Affine quiver, Bridgeland stability conditions on triangulated categories, Contractible space, Exceptional collections, Tame representation type quiver",

author = "George Dimitrov and Ludmil Katzarkov",

note = "Funding Information: The authors were funded by NSF DMS 0854977 FRG , NSF DMS 0600800 , NSF DMS 0652633 FRG , NSF DMS 0854977 , NSF DMS 0901330 , FWF P 24572 N25 , FWF P 25901 , FWF P 23665 , FWF P 20778 , an ERC GEMIS Grant, DMS-1265230 Wall Crossings in Geometry and Physics, DMS-1201475 Spectra Gaps Degenerations and Cycles, OISE-1242272 PASI On Wall Crossings Stability Hodge Structures & TQFT Grant. ",

year = "2016",

month = jan,

day = "22",

doi = "10.1016/j.aim.2015.10.014",

language = "English (US)",

volume = "288",

pages = "825--886",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

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T1 - Bridgeland stability conditions on the acyclic triangular quiver

AU - Dimitrov, George

AU - Katzarkov, Ludmil

N1 - Funding Information: The authors were funded by NSF DMS 0854977 FRG , NSF DMS 0600800 , NSF DMS 0652633 FRG , NSF DMS 0854977 , NSF DMS 0901330 , FWF P 24572 N25 , FWF P 25901 , FWF P 23665 , FWF P 20778 , an ERC GEMIS Grant, DMS-1265230 Wall Crossings in Geometry and Physics, DMS-1201475 Spectra Gaps Degenerations and Cycles, OISE-1242272 PASI On Wall Crossings Stability Hodge Structures & TQFT Grant.

PY - 2016/1/22

Y1 - 2016/1/22

N2 - Using results in our previous paper "Non-semistable exceptional objects in hereditary categories", we focus here on studying the topology of the space of Bridgeland stability conditions on Db(Repk(Q)), where Q= and k is an algebraically closed field. In particular, we prove that this space is contractible (in the previous paper it was shown that it is connected).

AB - Using results in our previous paper "Non-semistable exceptional objects in hereditary categories", we focus here on studying the topology of the space of Bridgeland stability conditions on Db(Repk(Q)), where Q= and k is an algebraically closed field. In particular, we prove that this space is contractible (in the previous paper it was shown that it is connected).

KW - Affine quiver

KW - Bridgeland stability conditions on triangulated categories

KW - Contractible space

KW - Exceptional collections

KW - Tame representation type quiver

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