Stratification of the space of foliations on CP2. (January 2016)

• Record Type: Journal Article
• Authors: Alcántara, Claudia R.
• Is Part Of: Journal of symbolic computation. Volume 72(2016)
• Page Start: 147
• Page End: 160
• Publication Date: 2016-01
• Subjects: Holomorphic foliation -- Degenerate singular point -- Stratification; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.02.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We describe an algorithm for constructing an algebraic stratification of the space of holomorphic foliations on CP 2 of degree d with respect to the action of Aut ( CP 2 ) by change of coordinates. The strata are non-singular, locally-closed algebraic varieties. We show that these varieties parameterize foliations with certain type of degenerate singular points. We give the explicit form of the foliation in some strata. We also obtain the dimension of these varieties.