Communications in Analysis and Geometry

Volume 18 (2010)

Number 4

Very twisted stable maps

Pages: 831 – 855



Qile Chen (Department of Mathematics, Brown University)

Steffen Marcus (Department of Mathematics, Brown University)

Henning Úlfarsson (School of Computer Science, Reykjavik University, Iceland)


Let $X$ be a smooth projective Deligne–Mumford stack overan algebraically closed field $k$ of characteristic $0$.In this paper, we construct the moduli stack$\widetilde{\sK}_{g,n}(X,\beta)$ of \emph{very twistedstable maps}, extending the notion of twisted stable mapsfrom \cite{AV} to allow for generic stabilizers on thesource curves. We also consider the Gromov–Witten theorygiven by this construction.

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