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Holomorphic curves in
exploded manifolds: regularity
Brett Parker |
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Geometry & Topology 23 (2019) 1621–1690
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Abstract |
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The category of exploded manifolds is an extension of the category of smooth manifolds; for exploded manifolds, some adiabatic limits appear as smooth families. This paper studies the equation on variations of a given family of curves in an exploded manifold. Roughly, we prove that the equation on variations of an exploded family of curves behaves as nicely as the equation on variations of a smooth family of smooth curves, even though exploded families of curves allow the development of normal-crossing or log-smooth singularities. The resulting regularity results are foundational to the author’s construction of Gromov–Witten invariants for exploded manifolds. |
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Keywords
holomorphic curves, exploded manifolds, regularity of dbar
equation, gluing analysis
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Mathematical Subject Classification 2010
Primary: 58J99
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References |
Publication
Received: 11 February 2011
Revised: 6 August 2018
Accepted: 22 October 2018
Published: 17 June 2019
Proposed: Tomasz Mrowka
Seconded: Peter Ozsváth, Dan Abramovich
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Authors |
| Brett Parker | |
| School of Mathematics Monash University Melbourne, VIC Australia |
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