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Bounds on Wahl singularities from symplectic topology

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Bounds on Wahl singularities from symplectic topology. / Evans, Jonathan David; Smith, Ivan.
In: Algebraic Geometry, Vol. 7, No. 1, 31.01.2020, p. 59-85.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Evans, JD & Smith, I 2020, 'Bounds on Wahl singularities from symplectic topology', Algebraic Geometry, vol. 7, no. 1, pp. 59-85. https://doi.org/10.14231/ag-2020-003

APA

Vancouver

Evans JD, Smith I. Bounds on Wahl singularities from symplectic topology. Algebraic Geometry. 2020 Jan 31;7(1):59-85. doi: 10.14231/ag-2020-003

Author

Evans, Jonathan David ; Smith, Ivan. / Bounds on Wahl singularities from symplectic topology. In: Algebraic Geometry. 2020 ; Vol. 7, No. 1. pp. 59-85.

Bibtex

@article{ad2bac063fed4ea1911185d50f655db9,
title = "Bounds on Wahl singularities from symplectic topology",
abstract = "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. ",
keywords = "symplectic topology, vanishing cycles, wahl singularities",
author = "Evans, {Jonathan David} and Ivan Smith",
year = "2020",
month = jan,
day = "31",
doi = "10.14231/ag-2020-003",
language = "English",
volume = "7",
pages = "59--85",
journal = "Algebraic Geometry",
issn = "2313-1691",
publisher = "EMS Press",
number = "1",

}

RIS

TY - JOUR

T1 - Bounds on Wahl singularities from symplectic topology

AU - Evans, Jonathan David

AU - Smith, Ivan

PY - 2020/1/31

Y1 - 2020/1/31

N2 - 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.

AB - 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.

KW - symplectic topology

KW - vanishing cycles

KW - wahl singularities

U2 - 10.14231/ag-2020-003

DO - 10.14231/ag-2020-003

M3 - Journal article

VL - 7

SP - 59

EP - 85

JO - Algebraic Geometry

JF - Algebraic Geometry

SN - 2313-1691

IS - 1

ER -