Header

UZH-Logo

Maintenance Infos

Block–Göttsche invariants from wall-crossing


Filippini, S A; Stoppa, J (2015). Block–Göttsche invariants from wall-crossing. Compositio Mathematica, 151(08):1543-1567.

Abstract

We show how some of the refined tropical counts of Block and Göttsche emerge from the wall-crossing formalism. This leads naturally to a definition of a class of putative<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0010437X14007994_inline1" xlink:type="simple" /><jats:tex-math>$q$</jats:tex-math></jats:alternatives></jats:inline-formula>-deformed Gromov–Witten invariants. We prove that this coincides with another natural<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0010437X14007994_inline2" xlink:type="simple" /><jats:tex-math>$q$</jats:tex-math></jats:alternatives></jats:inline-formula>-deformation, provided by a result of Reineke and Weist in the context of quiver representations, when the latter is well defined.

Abstract

We show how some of the refined tropical counts of Block and Göttsche emerge from the wall-crossing formalism. This leads naturally to a definition of a class of putative<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0010437X14007994_inline1" xlink:type="simple" /><jats:tex-math>$q$</jats:tex-math></jats:alternatives></jats:inline-formula>-deformed Gromov–Witten invariants. We prove that this coincides with another natural<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0010437X14007994_inline2" xlink:type="simple" /><jats:tex-math>$q$</jats:tex-math></jats:alternatives></jats:inline-formula>-deformation, provided by a result of Reineke and Weist in the context of quiver representations, when the latter is well defined.

Statistics

Citations

Dimensions.ai Metrics
9 citations in Web of Science®
9 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

3 downloads since deposited on 12 Oct 2018
3 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Scopus Subject Areas:Physical Sciences > Algebra and Number Theory
Language:English
Date:1 August 2015
Deposited On:12 Oct 2018 10:32
Last Modified:01 Aug 2020 00:00
Publisher:Cambridge University Press
ISSN:0010-437X
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1112/s0010437x14007994
Related URLs:https://www.swissbib.ch/Search/Results?lookfor=nationallicencecambridge101112S0010437X14007994 (Library Catalogue)

Download

Green Open Access

Download PDF  'Block–Göttsche invariants from wall-crossing'.
Preview
Content: Published Version
Language: English
Filetype: PDF (Nationallizenz 142-005)
Size: 814kB
View at publisher