The moduli space of stable quotients

By A. Marian, D. Oprea, R. Pandharipande. 2009

153 citations recorded by the source corpus.

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck’s Quot scheme. Over nodal curves, a relative construction is made to keep the torsion of the quotient away from the singularities. New compactifications of classical spaces arise naturally: a nonsingular and irreducible compactification of the moduli of maps from genus 1 curves to projective space is obtained. Localization on the moduli of stable quotients leads to new relations in the tautological ring generalizing Brill‐Noether constructions. The moduli space of stable quotients is proven to carry a canonical 2‐term obstruction theory and thus a virtual class. The resulting system of descendent invariants is proven to equal the Gromov‐Witten theory of the Grassmannian in all genera. Stable quotients can also be used to study Calabi‐Yau geometries. The conifold is calculated to agree with stable maps. Several questions about the behavior of stable quotients for arbitrary targets are raised. 14N35; 14C17 Dedicated to William Fulton on the occasion of his 70th birthday

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ef092a03d57cea522ea8be08644582afff0e2552

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Citations in the corpus

Segre classes and Hilbert schemes of points (2015, background): “In comparison, the intersection theory of the Quot scheme of a curve may be pursued in a virtual sense for a fixed curve [15] or by letting the curve vary via the moduli space of stable quotients [16].”
Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics (2019, background): “Many of the ideas developed here are related to collaborations with Alina Marian in [31, 32, 33, 34, 35, 36].”
Relations in the tautological ring of the moduli space of curves (2013, background): “The following result is proven in [13] by Quot scheme methods from the perspective of geometry relative to a divisor.”
Stable quasimaps to GIT quotients (2011, background): “ity condition allows base points, the obstruction theory will fail to be perfect if the singularities are worse than lci. In particular, this answers a question of Marian, Oprea, and Pandharipande in [35] by showing that the “moduli of stable quotients” to a projective subvariety X⊂Pn carries a natu”