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Moduli of Curves of Genus One with Twisted Fields

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arxiv 1906.10527 v2 pith:3XMFKZKA submitted 2019-06-25 math.AG

Yi Hu , Jingchen Niu This is my paper
classification math.AG
keywords genusmodulicurvesfieldsstabletwistedblowup-freeconstruction
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We construct a smooth Artin stack parameterizing the stable weighted curves of genus one with twisted fields and prove that it is isomorphic to the blowup stack of the moduli of genus one weighted curves studied by Hu and Li. This leads to a blowup-free construction of Vakil-Zinger's desingularization of the moduli of genus one stable maps to projective spaces. This construction provides the cornerstone of the theory of stacks with twisted fields, which is thoroughly studied in arXiv:2005.03384 and leads to a blowup-free resolution of the stable map moduli of genus two.

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  1. Higher genus reduced Gromov--Witten invariants via desingularizations of sheaves

    math.AG 2023-10 unverdicted novelty 5.0 of 10

    Two desingularization constructions for coherent sheaves on stacks are used to define reduced Gromov-Witten invariants of GIT quotients in higher genera.

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