Home > Research > Publications & Outputs > Antiflips, mutations, and unbounded symplectic ...

Research

Associated organisational unit

Electronic data

  • antiflips

    Accepted author manuscript, 524 KB, PDF document

    Available under license: CC BY-ND: Creative Commons Attribution-NoDerivatives 4.0 International License

Links

Text available via DOI:

Keywords

View graph of relations

Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls. / Evans, Jonny; Urzua, Giancarlo.
In: Annales de L'Institut Fourier, Vol. 71, No. 5, 31.12.2022, p. 1807-1843.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Evans, J & Urzua, G 2022, 'Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls', Annales de L'Institut Fourier, vol. 71, no. 5, pp. 1807-1843. https://doi.org/10.5802/aif.3429

APA

Evans, J., & Urzua, G. (2022). Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls. Annales de L'Institut Fourier, 71(5), 1807-1843. https://doi.org/10.5802/aif.3429

Vancouver

Evans J, Urzua G. Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls. Annales de L'Institut Fourier. 2022 Dec 31;71(5):1807-1843. Epub 2021 Dec 15. doi: 10.5802/aif.3429

Author

Evans, Jonny ; Urzua, Giancarlo. / Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls. In: Annales de L'Institut Fourier. 2022 ; Vol. 71, No. 5. pp. 1807-1843.

Bibtex

@article{8f669916c9ff4a289a7494d5c15324b8,
title = "Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls",
abstract = "The Milnor fibre of a Q-Gorenstein smoothing of a Wahl singularity is a rational homology ball B_{p,q}. For a canonically polarised surface of general type X, it is known that there are bounds on the number p for which B_{p,q} admits a symplectic embedding into X. In this paper, we give a recipe to construct unbounded sequences of symplectically embedded B_{p,q} into surfaces of general type equipped with non-canonical symplectic forms. Ultimately, these symplectic embeddings come from Mori's theory of flips, but we give an interpretation in terms of almost toric structures and mutations of polygons. The key point is that a flip of surfaces, as studied by Hacking, Tevelev and Urz{\'u}a, can be formulated as a combination of mutations of an almost toric structure and deformation of the symplectic form.",
keywords = "Singularities, MMP, symplectic geometry, almost toric manifolds",
author = "Jonny Evans and Giancarlo Urzua",
year = "2022",
month = dec,
day = "31",
doi = "10.5802/aif.3429",
language = "English",
volume = "71",
pages = "1807--1843",
journal = "Annales de L'Institut Fourier",
issn = "0373-0956",
publisher = "Association des Annales de l'Institut Fourier",
number = "5",

}

RIS

TY - JOUR

T1 - Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls

AU - Evans, Jonny

AU - Urzua, Giancarlo

PY - 2022/12/31

Y1 - 2022/12/31

N2 - The Milnor fibre of a Q-Gorenstein smoothing of a Wahl singularity is a rational homology ball B_{p,q}. For a canonically polarised surface of general type X, it is known that there are bounds on the number p for which B_{p,q} admits a symplectic embedding into X. In this paper, we give a recipe to construct unbounded sequences of symplectically embedded B_{p,q} into surfaces of general type equipped with non-canonical symplectic forms. Ultimately, these symplectic embeddings come from Mori's theory of flips, but we give an interpretation in terms of almost toric structures and mutations of polygons. The key point is that a flip of surfaces, as studied by Hacking, Tevelev and Urzúa, can be formulated as a combination of mutations of an almost toric structure and deformation of the symplectic form.

AB - The Milnor fibre of a Q-Gorenstein smoothing of a Wahl singularity is a rational homology ball B_{p,q}. For a canonically polarised surface of general type X, it is known that there are bounds on the number p for which B_{p,q} admits a symplectic embedding into X. In this paper, we give a recipe to construct unbounded sequences of symplectically embedded B_{p,q} into surfaces of general type equipped with non-canonical symplectic forms. Ultimately, these symplectic embeddings come from Mori's theory of flips, but we give an interpretation in terms of almost toric structures and mutations of polygons. The key point is that a flip of surfaces, as studied by Hacking, Tevelev and Urzúa, can be formulated as a combination of mutations of an almost toric structure and deformation of the symplectic form.

KW - Singularities

KW - MMP

KW - symplectic geometry

KW - almost toric manifolds

U2 - 10.5802/aif.3429

DO - 10.5802/aif.3429

M3 - Journal article

VL - 71

SP - 1807

EP - 1843

JO - Annales de L'Institut Fourier

JF - Annales de L'Institut Fourier

SN - 0373-0956

IS - 5

ER -