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This article is cited in 11 scientific papers (total in 11 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.
Received: March 13, 2008
Citation:
Arend Bayer, Yu. I. Manin, “Stability conditions, wall-crossing and weighted Gromov–Witten invariants”, Mosc. Math. J., 9:1 (2009), 3–32
Linking options:
https://www.mathnet.ru/eng/mmj334 https://www.mathnet.ru/eng/mmj/v9/i1/p3
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