Arithmetic families of smooth surfaces and equisingularity of embedded schemes |
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| Authors: | Augusto Nobile Orlando E Villamayor |
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| Institution: | Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA. e-mail: nobile@math.lsu.edu, US
Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, E-28049 Madrid, Espa?a. e-mail: villamayor@uam.es, ES
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| Abstract: | This article deals with the foundations of a theory of equisingularity for families of zero-dimensional sheaves of ideals
on smooth algebraic surfaces, in the arithmetic context, i.e., where one works with schemes defined over Dedekind rings. Here,
different equisingularity conditions are analyzed and compared, based on one of the following requirements: 1) each member
of the the family has the same desingularization tree, 2) the family admits a simultaneous desingularization, 3) a naturally
associated family of curves is equisingular. Similar conditions had been investigated, in the context of Complex Local Analytic
Geometry, by J. J. Risler.
Received: 17 November 1997 / Revised version: 19 April 1999 |
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| Keywords: | Mathematics Subject Classification (1991):14B05 14D99 13C05 |
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