Stable Morphisms to Singular Schemes and Relative Stable Morphisms

By Jun Li. 2001

122 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3ff0f5494aa8f0227ed7e64f371206efe097c65a

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quivers, curves, and the tropical vertex (2009, background): “We refer the reader to Section 1 of [14] for an introduction to the destabilizations required for stable relative maps.”
Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, background): “One can think of them as corresponding to strata in the space of relative stable maps [25] to (F,M), which have degree 2 over CP .”
Toric degenerations of toric varieties and tropical curves (2004, background): “In the proof of the Main Theorem in Section 8 we will see that (ii) is indeed a necessary condition for a torically transverse curve to deform in the family π. The necessity of such a condition in a similar context was first pointed out by Tian [Ti], and it occurs at prominent place in Jun Li’s work”
admcycles - a Sage package for calculations in the tautological ring of the moduli space of stable curves (2020, unknown): “…been defined as the pushforward of the virtual fundamental class of a space of maps to rubber P1 102 Delecroix, Schmitt and van Zelm :::: admcycles Sage package relative to 0,∞ with tangency conditions at 0,∞ specified by the vector A (see [Li and Ruan 2001; Li 2002; 2001; Graber and Vakil 2005]).”
Affine manifolds, log structures, and mirror symmetry (2002, result): “Previous general work in this direction is due to Tian; Li and Ruan [21]; Ionel and Parker [15]; Gathmann [6] and Li [22],[23], who covers cases relative a smooth divisor and of normal crossing varieties with smooth singular locus.”
A Degeneration Formula of GW-Invariants (2001, methodology): “. To achieve this, we need to construct a new relative moduli space of stable morphisms to W/C. This is achieved by reﬁning the notion of stable morphisms, worked out in the ﬁrst part of this project [Li]. Recall that in [Li] we constructed a stack W that includes all expanded degenerations of W. We”
Hodge Integrals and Hurwitz Numbers via Virtual Localization (2000, background): “Proof. A general cycle g 2 L1 representing p is the sum of r distinct points plus the point 1 exactly k times.”