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Moduli of Curves of Genus One with Twisted Fields
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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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Irreducible components of moduli spaces of maps to smooth projective toric varieties in genus 0
The irreducible components of genus-0 stable map spaces to toric varieties are indexed by stable decorated trees that maximize a combinatorial invariant d_GGG.
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