Intersection Theory on Abelian-Quotient V-Surfaces and Q-Resolutions

Enrique Artal Bartolo, Jorge Martín-Morales, and Jorge Ortigas-Galindo

Journal of Singularities
volume 8 (2014), 11-30

Received: 11 July 2013. Received in revised form: 25 February 2014.

DOI: 10.5427/jsing.2014.8b

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Abstract:

In this paper we study the intersection theory on surfaces with abelian quotient singularities and we obtain formulas for its behavior under weighted blow-ups. As applications, we extend Mumford's formulas for the intersection theory on normal divisors, we derive properties for quotients of weighted projective planes, and finally, we compute abstract Q-resolutions of normal surfaces using Jung's method.

Keywords:

Quotient singularity, intersection number, embedded Q-resolution

Mathematical Subject Classification:

Primary: 32S25; Secondary: 32S45

Author(s) information:

Enrique Artal Bartolo	Jorge Martín-Morales	Jorge Ortigas-Galindo
Departamento de Matemáticas-IUMA	Centro Universitario de la Defensa-IUMA	Centro Universitario de la Defensa-IUMA
Universidad de Zaragoza	Academia General Militar	Academia General Militar
C/ Pedro Cerbuna 12	Ctra.de Huesca s/n	Ctra.de Huesca s/n
50009, Zaragoza, Spain	50090, Zaragoza, Spain	50090, Zaragoza, Spain
email: artal@unizar.es	email: jorge@unizar.es	email: jortigas@unizar.es