Expanded Degenerations and Pairs
By D. Abramovich, Charles Cadman, Barbara Fantechi, Jonathan Wise. 2011
47 citations recorded by the source corpus.
We provide a universal approach to the moduli of Jun Li's expanded pairs and expanded degenerations [20]. This enables us to prove algebraicity results, compare with Li's approach and with the approach of Graber and Vakil [16], and generalize to the twisted expansions used by Abramovich and Fantechi as a basis for orbifold techniques in degeneration formulas.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/886be33e0ab97bbea9b24421ad30794c4c7a1e6d
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In Geometry and Topology
- D. Abramovich
- Jonathan Wise
- Qile Chen
- Steffen Marcus
- Dhruv Ranganathan
- Barbara Fantechi
- Martin Ulirsch
- David Jensen
In Mathematical Physics
- D. Abramovich
- Qile Chen
- Jonathan Wise
- Steffen Marcus
- Barbara Fantechi
- Dhruv Ranganathan
- Martin Ulirsch
- David Jensen
Citations in the corpus
- Orbifold techniques in degeneration formulas (2011, methodology): “ng the identification of D′ 1 with D ′ 2 via β. We let D′ be the closed substack image of either D′ i. Remark 1.4.2. A generalization of this construction and more information about it may be found in [ACFW] and [BV]. ORBIFOLD TECHNIQUES IN DEGENERATION FORMULAS 17 1.4.3. Gluing as pushout. In Definit”
- Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations (2012, methodology): “bal geometry of X/V. It is possible to isolate this global geometry by comparing the space of maps to X/V with the space of maps to a universal target X /V . This method was introduced in [ACW10] and [ACFW13] and has been used in [CMW12] as well. The universal targets are defined as follows: (1) The ”
- Skeletons and Fans of Logarithmic Structures (2015, methodology): “ce an Artin fan Ais logarithmically etale, a map f: C!A X from a curve to A X is logarithmically unobstructed. Precursors to this result for specic X were obtained in [ACFW13,ACW10,AMW14,CMW12]. In [ACFW13] an approach to Jun Li’s expanded degenerations was provided using what in hindsight we might ”