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  • 1708.02268

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Bounds on Wahl singularities from symplectic topology

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<mark>Journal publication date</mark>31/01/2020
<mark>Journal</mark>Algebraic Geometry
Issue number1
Number of pages27
Pages (from-to)59-85
Publication StatusPublished
<mark>Original language</mark>English


Let X be a minimal surface of general type with positive geometric genus (b+>1) and let K2 be the square of its canonical class. Building on work of Khodorovskiy and Rana, we prove that if X develops a Wahl singularity of length ℓ in a Q-Gorenstein degeneration, then ℓ≤4K2+7. This improves on the current best-known upper bound due to Lee (ℓ≤400(K2)4). Our bound follows from a stronger theorem constraining symplectic embeddings of certain rational homology balls in surfaces of general type. In particular, we show that if the rational homology ball Bp,1 embeds symplectically in a quintic surface, then p≤12, partially answering the symplectic version of a question of Kronheimer.