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

Dan AbramovichSteffen MarcusJonathan Wise — 2014

Annales de l’institut Fourier

We consider four approaches to relative Gromov–Witten theory and Gromov–Witten theory of degenerations: J. Li’s original approach, B. 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...

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