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arXiv · 1005.3743

Moduli spaces of stable quotients and wall-crossing phenomena

Yukinobu Toda
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Abstract

The moduli space of holomorphic maps from Riemann surfaces to the Grassmannian is known to have two kinds of compactifications: Kontsevich's stable map compactification and Marian-Oprea-Pandharipande's stable quotient compactification. Over a non-singular curve, the latter moduli space is Grothendieck's Quot scheme. In this paper, we give the notion of `$ε$-stable quotients' for a positive real number $ε$, and show that stable maps and stable quotients are related by the wall-crossing phenomena. We will also discuss Gromov-Witten type invariants associated to $ε$-stable quotients, and investigate them under the wall-crossing.

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Yukinobu Toda. 2011-10-03. Moduli spaces of stable quotients and wall-crossing phenomena. https://doi.org/10.1112/s0010437x11005434

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