Log geometry and exploded manifolds
arXiv:1108.3713
Abstract
Log Gromov-Witten invariants have recently been defined separately by Gross and Siebert and Abramovich and Chen. This paper provides a dictionary between log geometry and holomorphic exploded manifolds in order to compare Gromov-Witten invariants defined using exploded manifolds or log schemes. The gluing formula for Gromov-Witten invariants of exploded manifolds suggests an approach to proving analogous gluing formulas for log Gromov-Witten invariants.
v4: In previous versions, I used C[Q/Q'] to mean the quotient of C[Q] by the ideal generated by Q' in the mistaken belief that this was equal to the monoid ring over Q/Q'. The offending notation is now fixed
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