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Cayley–Bacharach and Singularities of Foliations.
- Source :
-
Bulletin of the Brazilian Mathematical Society . Sep2021, Vol. 52 Issue 3, p477-498. 22p. - Publication Year :
- 2021
-
Abstract
- This paper deals with foliations by curves [s] of degree r ≥ 2 on P 2 with isolated singularities S, called non-degenerate if S is reduced and otherwise degenerate. Say that [s] is uniquely determined by a zero-dimensional Y ⊂ S if [s] is the unique foliation that vanishes on Y and say that Y is minimal for [s] if, moreover, the degree of Y is the minimal possible to do so. Previous work of the authors show that every non-degenerate foliation in degrees 2 ≤ r ≤ 5 does have a minimal subscheme and that the set of non-degenerate foliations of degree r ≥ 6 that have a minimal subscheme contains a Zariski-open subset of the space of foliations of degree r. For non-degenerate foliations [s] we present both characterizations and sufficient conditions for [s] to have a minimal subscheme. We also give examples of degenerate foliations of degree r ≥ 7 that do not have a minimal subscheme at all. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FOLIATIONS (Mathematics)
*PROJECTIVE planes
Subjects
Details
- Language :
- English
- ISSN :
- 16787544
- Volume :
- 52
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Brazilian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 151566670
- Full Text :
- https://doi.org/10.1007/s00574-020-00214-9