# ANNALES DE L'INSTITUT FOURIER

Quotient singularities of products of two curves
Annales de l'Institut Fourier, Volume 71 (2021) no. 4, pp. 1493-1534.

We give a method to resolve a quotient surface singularity which arises as the quotient of a product action of a finite group on two curves. In the characteristic zero case, the singularity is resolved by means of a continued fraction, which is known as the Hirzebruch–Jung desingularization. We develop the method in the positive characteristic case where the square of the characteristic does not divide the order of the group.

Nous donnons une méthode pour résoudre une singularité quotient de surface qui se présente comme le quotient d’une action produit d’un groupe fini sur deux courbes. En caractéristique nulle, la singularité est résolue au moyen d’une fraction continue (désingularisation de Hirzebruch–Jung). Nous développons la méthode dans le cas de la caractéristique strictement positive où le carré de la caractéristique ne divise pas l’ordre du groupe.

Revised:
Accepted:
Online First:
Published online:
DOI: 10.5802/aif.3434
Classification: 14J17,  14B05,  14M25,  14G17
Keywords: surface singularity, positive characteristic, wild quotient, desingularization, partial desingularization, toric geometry
Mitsui, Kentaro 1

1 Department of Mathematics Graduate School of Science Kobe University Hyogo 657-8501 (Japan)
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Mitsui, Kentaro. Quotient singularities of products of two curves. Annales de l'Institut Fourier, Volume 71 (2021) no. 4, pp. 1493-1534. doi : 10.5802/aif.3434. https://aif.centre-mersenne.org/articles/10.5802/aif.3434/

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