RT info:eu-repo/semantics/article
T1 Invariant surfaces for toric type foliations in dimension three
A1 Molina Samper, Beatriz
A1 Cano Torres, Felipe
K1 Foliación
K1 Singular foliations
K1 Invariant surfaces
K1 Toric varieties
K1 Combinatorial blowing-ups.
K1 1201.01 Geometría Algebraica
AB A foliation is of toric type when it has a combinatorial reduction of singularities. We show that every toric type foliation on (C3, 0) without saddle-nodes has invariant surface. We extend the argument of Cano–Cerveau for the nondicritical case to the compact dicritical components of the exceptional divisor. These components are projective toric surfaces and the isolated invariant branches of the induced foliation extend to closed irreducible curves. We build the invariant surface as a germ along the singular locus and those closed irreducible invariant curves. The result of Ortiz-Bobadilla & Rosales-González &Voronin about the distribution of invariant branches in dimension two is a key argument in our proof.
PB Universitat Autònoma de Barcelona
SN 0214-1493
YR 2021
FD 2021
LK https://uvadoc.uva.es/handle/10324/70835
UL https://uvadoc.uva.es/handle/10324/70835
LA eng
NO Publicacions Matemàtiques, 2021 vol. 65,  n.1,  pp. 291-307
DS UVaDOC
RD 23-dic-2024