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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 · ORCID
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 2 Pith papers

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

  1. Irreducible components of moduli spaces of maps to smooth projective toric varieties in genus 0

    math.AG 2025-06 conditional novelty 8.0 of 10

    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.

  2. 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.

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