The Kupka Scheme and Unfoldings
Let ω be a differential 1-form defining an algebraic foliation of codimension 1 in projective space. In this article we use commutative algebra to study the singular locus of ω through its ideal of definition. Then, we expose the relation between the ideal defining the Kupka components of the singul...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/103603 |
| Acceso en línea: | http://hdl.handle.net/11336/103603 |
| Access Level: | acceso abierto |
| Palabra clave: | Unfoldings of foliations Kupka set algebraic foliations https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Let ω be a differential 1-form defining an algebraic foliation of codimension 1 in projective space. In this article we use commutative algebra to study the singular locus of ω through its ideal of definition. Then, we expose the relation between the ideal defining the Kupka components of the singular set of ω and the first order unfoldings of ω. Exploiting this relation, we show that the set of Kupka points of ω is generically not empty. As an application of these results, we can compute the ideal of first order unfoldings for some known components of the space of foliations. |
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