Logarithmic Stable Maps
By Bumsig Kim. 2008
56 citations recorded by the source corpus.
We introduce the notion of a logarithmic stable map from a minimal log prestable curve to a log twisted semi-stable variety of form $xy=0$. We study the compactification of the moduli spaces of such maps and provide a perfect obstruction theory, applicable to the moduli spaces of (un)ramified stable maps and stable relative maps. As an application, we obtain a modular desingularization of the main component of Kontsevich's moduli space of elliptic stable maps to a projective space.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5c2392c94d37951d170f3d1667956f99fbd05835
How researchers see this paper
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In Geometry and Topology
- D. Abramovich
- Dhruv Ranganathan
- Qile Chen
- Jonathan Wise
- Steffen Marcus
- Charles Cadman
- Matthew Satriano
- D. Gillam
In Mathematical Physics
- Dhruv Ranganathan
- D. Abramovich
- Qile Chen
- Jonathan Wise
- Steffen Marcus
- Charles Cadman
- Matthew Satriano
- D. Gillam
Citations in the corpus
- Logarithmic Geometry and Moduli (2010, background): “This is where Bumsig Kim’s paper [33] comes in: he provides a correct formalism for nondegenerate logarithmic stable maps into expanded degenerations, and shows that it carries a perfect obstruction theory.”
- Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations (2012, methodology): “After the logarithmic cotangent complex became available in the work of Olsson [32], Kim used it to study logarithmic maps from curves into expanded targets [26], giving another means to avoid predeformability.”
- Stable logarithmic maps to Deligne-Faltings pairs I (2010, background): “A degeneration formula under Kim’s setting is proved in [Chen].”
- Relative and orbifold Gromov-Witten invariants (2010, background): “We will not discuss logarithmic stable maps here, but see [Kim08] for some of the beginnings of this theory.”
- Logarithmic Gromov–Witten theory with expansions (2019, methodology): “Assume the existence of the moduli space Kim of logarithmic maps to expansions of the universal target [A(1)/Gm], as in [42].”