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Castelnuovo's bound and rigidity in almost complex geometry

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arxiv 1809.04731 v2 pith:JWGNLR4O submitted 2018-09-13 math.SG math.DG

Aleksander Doan , Thomas Walpuski This is my paper · ORCID
classification math.SGmath.DG
keywords boundalmostcomplexmanifoldsarticlecalabi-yaucastelnuovocompactness
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This article is concerned with the question of whether an energy bound implies a genus bound for pseudo-holomorphic curves in almost complex manifolds. After reviewing what is known in dimensions other than 6, we establish a new result in this direction in dimension 6; in particular, for symplectic Calabi-Yau 6-manifolds. The proof relies on compactness and regularity theorems for J-holomorphic currents.

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  1. Curvy points, the perimeter, and the complexity of convex toric domains

    math.SG 2025-06 conditional novelty 7.0 of 10

    For any convex toric domain, the liminf of the subleading ECH capacities equals minus half the affine perimeter, yielding new packing obstructions and a classification of smooth toric domains with infinite staircases.

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