arXiv subjects

Jingchen Niu

Publications and source records attributed to Jingchen Niu.

4 recordsLinked to original sources

arXiv2020

Moduli of Curves of Genus One with Twisted Fields

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.

math.AG↗

arXiv2020

A theory of stacks with twisted fields and resolution of moduli of genus two stable maps

We construct a smooth algebraic stack of tuples consisting of genus two nodal curves, simple effective divisors away from the nodes, and twisted fields. It provides a desingularization of the moduli of genus two stable maps to projective spaces. The construction is based on systematic application of the theory of stacks with twisted fields (STF), which has its prototype appeared in arXiv:1201.2427 and arXiv:1906.10527 and is fully developed in this article. As a byproduct of the STF theory, we also obtain a novel desingularization of the moduli of genus one stable maps to projective spaces, which is isomorphic to the blowup that reverses the order used by Vakil-Zinger and Hu-Li. The results of this article are the second step of a program toward the resolutions of the moduli of stable maps of higher genera.

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arXiv2015

Lower Bounds for Enumerative Counts of Positive-Genus Real Curves

We transform the positive-genus real Gromov-Witten invariants of many real-orientable symplectic threefolds into signed counts of curves. These integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints. We conclude with some implications and related conjectures for one- and two-partition Hodge integrals.

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arXiv2012

Genus Two Stable Maps, Local Equations and Modular Resolutions

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.

math.AG↗