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Toda, Yukinobu

Moduli space of stable quotients and wall-crossing phenomena. (English) Zbl 1236.14049

Compos. Math. 147, No. 5, 1479-1518 (2011).
The author investigates wall-crossing phenomena of several compactifications of the moduli spaces of holomorphic maps from Riemann surfaces to the Grassmannian. More explicitly, the author introduces the notion of \(\epsilon\)-stable quotients for a positive real number \(\epsilon\), and proves that the moduli space of \(\epsilon\)-stable quotients is a proper Deligne-Mumford stack over \(\mathbb{C}\) with perfect obstruction theory. The author also proves that stable quotients and stable maps are related by a wall-crossing phenomena.
A discussion of Gromov-Witten type invariants associated to \(\epsilon\)-stable quotients and their behavior under wall-crossing can be found in this article.
Reviewer: Vehbi Emrah Paksoy (Fort Lauderdale)

Cited in 17 Documents

MSC:

14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14H60 Vector bundles on curves and their moduli

Keywords:

Quot scheme; Gromov-Witten invariant; wall-crossing; stable quotient
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References:

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