Comparison theorems for Gromov-Witten invariants of smooth pairs and of degenerations

Autor:	Abramovich, D., Marcus, S., JONATHAN WISE
Rok vydání:	2012
Předmět:	Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 14N35 14H10 14D23 14D06 14A20 FOS: Mathematics Mathematics::Symplectic Geometry Algebraic Geometry (math.AG)
Zdroj:	Scopus-Elsevier
DOI:	10.48550/arxiv.1207.2085
Popis:	We consider four approaches to relative Gromov-Witten theory and Gromov-Witten theory of degenerations: Jun Li's original approach, Bumsig Kim's logarithmic expansions, Abramovich-Fantechi's orbifold expansions, and a logarithmic theory without expansions due to Gross-Siebert and Abramovich-Chen. We exhibit morphisms relating these moduli spaces and prove that their virtual fundamental classes are compatible by pushforward through these morphisms. This implies that the Gromov-Witten invariants associated to all four of these theories are identical. Comment: 42 pages. Some minor changes. To appear in Annales de l'Institut Fourier
Databáze:	OpenAIRE
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