Stable logarithmic maps to Deligne-Faltings pairs II

By D. Abramovich, Qile Chen. 2014

188 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e6f13bfa6e90a3b7eeb005695a4e74a2f034b811

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In Geometry and Topology

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Citations in the corpus

Logarithmic Gromov–Witten theory with expansions (2019, methodology): “can be applied to construct the spaces in Theorem A in a manner that is logically independent from the foundational papers in logarithmic Gromov–Witten theory [2, 20, 30], and this is explained by Carocci–Nabijou [15].”
Stable logarithmic maps to Deligne-Faltings pairs I (2010, methodology): “This point of view will be a useful tool in [AC11], where we reduce the case with generalized DF-log structure on the target to the case of this paper.”
Decomposition of degenerate Gromov–Witten invariants (2017, methodology): “ X. 2.3. Stable logarithmic maps and their moduli. 2.3.1. Denition. We x a log morphism X!Bwith the logarithmic structure on X being dened in the Zariski topology. Recall from [GS13], [Che14] and [AC14]: DECOMPOSITION OF DEGENERATE GROMOV-WITTEN INVARIANTS 11 Denition 2.3.2. A stable logarithmic ma”
Descendant log Gromov-Witten invariants for toric varieties and tropical curves (2016, methodology): “n as above. By replacing N with 1 dN⊂ NQ for some d∈ Z>0, we can assume that P is integral. 3.2. The moduli space. Let f †: Y → S† be a log smooth morphism of ﬁne saturated log schemes. [GS13] and [AC14] show that the stack M(Y/S) of basic6 stable log maps to Y† over S† is a DeligneMumford log st”
Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations (2012, methodology): “The impact of the degeneration formula has been profound, but efforts to generalize the theory to other degenerations have until recently met with limited success (see [34, 33, 16, 20, 3] for recent progress).”
Brill-Noether theory for curves of a fixed gonality (2017, methodology): “ND TROPICAL The proof of the main lifting theorems, as well as the analysis of generic chains of cycles in the following section, will use the geometryof logarithmic prestable maps to toric varieties [2, 17, 28] and their relationship to Berkovich geometry [45, 46, 50]. We provide a rapid overview o”