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Abstract: The category of exploded manifolds is an extension of the category of smoothmanifolds related to tropical geometry in which some adiabatic limits appear assmooth families. This paper studies the dbar equation on variations of a givenfamily of curves in an exploded manifold. Roughly, we prove that the dbarequation on variations of an exploded family of curves behaves as nicely as thedbar equation on variations of a smooth family of smooth curves, even thoughexploded families of curves allow the development of normal crossing or logsmooth singularities. The resulting regularity results are used in a series ofseparate papers to construct Gromov Witten invariants for exploded manifolds.



Autor: Brett Parker

Fuente: https://arxiv.org/







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