Genus-One Stable Maps, Local Equations, and Vakil-Zinger's desingularization
Yi Hu, Jun Li
TL;DR
This paper presents an algebraic geometric method for desingularizing the main component of genus one stable maps moduli space, offering detailed local structure insights and potential extensions to higher genera.
Contribution
It introduces a new algebraic approach to Vakil-Zinger's desingularization, providing comprehensive local structural results for the moduli space.
Findings
Complete local structural descriptions of the moduli space
Desingularization of the entire moduli space
Framework extendable to higher genera
Abstract
We describe an algebro-geometric approach to Vakil-Zinger's desingularization of the main component of the moduli of genus one stable maps to projective space. The new approach provides complete local structural results for this moduli space as well as for the desingularization of the entire moduli space and should fully extend to higher genera.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Advanced Topics in Algebra