Very twisted stable maps

Communications in Analysis and Geometry, Volume 18, Number 4. (2010)

Qile, Steffen and Henning

Let X be a smooth projective Deligne-Mumford stack over an algebraically closed field k of characteristic 0. In this paper we construct the moduli stack of very twisted stable maps, extending the notion of twisted stable maps by Abramovich and Vistoli to allow for generic stabilizers on the source curves. We also consider the Gromov-Witten theory given by this construction.

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• Communications in Analysis and Geometry, Volume 18, Number 4. (2010)
• arXiv

Presentations

Later work (last updated 2 October 2026)

• D. Ross and Z. Zong, The gerby Gopakumar–Mariño–Vafa formula, Geom. Topol. 17 (2013). Suggests very twisted stable maps as a way to keep track of gerby data in orbifold Gromov–Witten theory.
• D. Cheong, The stack of gerbes in a quotient stack, J. Chungcheong Math. Soc. 32 (2019). Shows that when $X$ is a quotient stack, the stack of gerbes $\mathcal{G}_X$ constructed here is a quotient stack too.
• All citing papers on Google Scholar (3)