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Effective algebraic geometry and normal forms of reversible mappings.

Alain Jacquemard, Marco Antonio Teixeira (2002)

Revista Matemática Complutense

We present a new method to compute normal forms, applied to the germs of reversible mappings. We translate the classification problem of these germs to the theory of ideals in the space of the coefficients of their jets. Integral factorization coupled with Gröbner basis constructionjs the key factor that makes the process efficient. We also show that a language with typed objects like AXIOM is very convenient to solve these kinds of problems.

Equimultiple Locus of Embedded Algebroid Surfaces and Blowing–up in Characteristic Zero

Piedra-Sánchez, R., Tornero, J. (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 14B05, 32S25.The smooth equimultiple locus of embedded algebroid surfaces appears naturally in many resolution processes, both classical and modern. In this paper we explore how it changes by blowing–up.* Supported by FQM 304 and BFM 2000–1523. ** Supported by FQM 218 and BFM 2001–3207.

Equivariant virtual Betti numbers

Goulwen Fichou (2008)

Annales de l’institut Fourier

We define a generalised Euler characteristic for arc-symmetric sets endowed with a group action. It coincides with the Poincaré series in equivariant homology for compact nonsingular sets, but is different in general. We put emphasis on the particular case of / 2 , and give an application to the study of the singularities of Nash function germs via an analog of the motivic zeta function of Denef and Loeser.

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