6533b85bfe1ef96bd12ba6aa
RESEARCH PRODUCT
Local monomialization of generalized real analytic functions
Rafael Martín Villaverdesubject
[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]resolution of singularitiesRésolution des singularités[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM][MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Local monomializationUniformisation locale[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM][MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]local uniformization[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]description
Generalized power series extend the notion of formal power series by considering exponents ofeach variable ranging in a well ordered set of positive real numbers. Generalized analytic functionsare defined locally by the sum of convergent generalized power series with real coe cients. Weprove a local monomialization result for these functions: they can be transformed into a monomialvia a locally finite collection of finite sequences of local blowingsup. For a convenient frameworkwhere this result can be established, we introduce the notion of generalized analytic manifoldand the correct definition of blowing-up in this category.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-12-15 |