Moduli space of stable quotients and wall-crossing phenomena. (English) Zbl 1236.14049
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.
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)
MSC:
14N35 | Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) |
14H60 | Vector bundles on curves and their moduli |
References:
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