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Genus Two Stable Maps, Local Equations and Modular Resolutions

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arxiv 1201.2427 v4 pith:MC7LZ75Y submitted 2012-01-11 math.AG

Yi Hu , Jun Li , Jingchen Niu This is my paper
classification math.AG
keywords mapsspacestablegenus-twomodularmodulisingularitiesstack
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We provide a geometric construction of a sequence of modular blowups of the Artin stack parameterizing pre-stable pairs consisting of a genus-two nodal curve and a smooth divisor. The resulting stack locally diagonalizes the tautological derived objects associated with the moduli of stable maps from genus-two curves to projective space. As a consequence, the singularities of the main component of the moduli space of stable maps are resolved, and the entire space admits only normal crossing singularities. Our approach is expected to generalize to higher genera.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Reduced Gromov-Witten invariants without ghost bubble censorship

    math.SG 2026-04 unverdicted novelty 7.0 of 10

    Defines all-genus reduced Gromov-Witten invariants of symplectic manifolds via effectively supported multivalued perturbations on derived orbifold/Kuranishi charts, bypassing ghost bubble censorship.

  2. Reduced Gromov-Witten invariants without ghost bubble censorship

    math.SG 2026-04 conditional novelty 7.0 of 10

    All-genus reduced Gromov–Witten invariants are defined for compact symplectic manifolds via normally complex stratified multisections on Kuranishi atlases.

  3. 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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