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Mosc. Math. J., 2009, Volume 9, Number 1, Pages 3–32 (Mi mmj334)  

This article is cited in 9 scientific papers (total in 9 papers)

Stability conditions, wall-crossing and weighted Gromov–Witten invariants

Arend Bayerab, Yu. I. Maninac

a Max-Planck-Institut für Mathematik, Bonn, Germany
b Mathematical Sciences Research Institute, Berkeley, CA
c North-western University, Evanston, USA

Abstract: We extend B. Hassett's theory of weighted stable pointed curves to weighted stable maps. The space of stability conditions is described explicitly, and the wall-crossing phenomenon studied. This can be considered as a non-linear analog of the theory of stability conditions in abelian and triangulated categories (cf. works by A. Gorodentsev, S. Kuleshov, and A. Rudakov, T. Bridgeland, D. Joyce).
We introduce virtual fundamental classes and thus obtain weighted Gromov–Witten invariants. We show that by including gravitational descendants, one obtains an $L$-algebra as introduced by A. Losev and Yu. Manin as a generalization of a cohomological eld theory.

Key words and phrases: weighted stable maps, gravitational descendants.

DOI: https://doi.org/10.17323/1609-4514-2009-9-1-3-32

Full text: http://www.ams.org/.../abst9-1-2009.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 14N35, 14D22; Secondary 53D45, 14H10, 14E99
Received: March 13, 2008
Language:

Citation: Arend Bayer, Yu. I. Manin, “Stability conditions, wall-crossing and weighted Gromov–Witten invariants”, Mosc. Math. J., 9:1 (2009), 3–32

Citation in format AMSBIB
\Bibitem{BayMan09}
\by Arend~Bayer, Yu.~I.~Manin
\paper Stability conditions, wall-crossing and weighted Gromov--Witten invariants
\jour Mosc. Math.~J.
\yr 2009
\vol 9
\issue 1
\pages 3--32
\mathnet{http://mi.mathnet.ru/mmj334}
\crossref{https://doi.org/10.17323/1609-4514-2009-9-1-3-32}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2567394}
\zmath{https://zbmath.org/?q=an:05642247}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000269218000001}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bayer A., Cadman Ch., “Quantum cohomology of $[\mathbb C^N/\mu_r]$”, Compos. Math., 146:5 (2010), 1291–1322  crossref  mathscinet  zmath  isi  scopus
    2. Shadrin S., Zvonkine D., “A Group Action on Losev-Manin Cohomological Field Theories”, Ann. Inst. Fourier, 61:7 (2011), 2719–2743  crossref  mathscinet  zmath  isi
    3. Viscardi M., “Alternate Compactifications of the Moduli Space of Genus One Maps”, Manuscr. Math., 139:1-2 (2012), 201–236  crossref  mathscinet  zmath  isi  scopus
    4. Manolache C., “Stable Maps and Stable Quotients”, Compos. Math., 150:9 (2014), 1457–1481  crossref  mathscinet  zmath  isi  scopus
    5. Manin Yu.I., Smirnov M., “Towards Motivic Quantum Cohomology of (M)Over-Bar(0,S)”, Proc. Edinb. Math. Soc., 57:1 (2014), 201–230  crossref  mathscinet  zmath  isi  scopus
    6. Ulirsch M., “Tropical Geometry of Moduli Spaces of Weighted Stable Curves”, J. Lond. Math. Soc.-Second Ser., 92:2 (2015), 427–450  crossref  mathscinet  zmath  isi  scopus
    7. Ciocan-Fontanine I., Kim B., “Big i-Functions”, Development of Moduli Theory - Kyoto 2013, Advanced Studies in Pure Mathematics, 69, eds. Fujino O., Kondo S., Moriwaki A., Saito M., Yoshioka K., Math Soc Japan, 2016, 323–347  mathscinet  zmath  isi
    8. Abramovich D., Fantechi B., “Configurations of Points on Degenerate Varieties and Properness of Moduli Spaces”, Rend. Semin. Mat. Univ. Padova, 137 (2017), 1–17  crossref  mathscinet  zmath  isi  scopus
    9. Sharma N., “Psi-Class Intersections on Hassett Spaces For Genus 0 With All Weights 1/2”, Rocky Mt. J. Math., 49:7 (2019), 2297–2324  crossref  mathscinet  zmath  isi  scopus
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