TY - JOUR
T1 - An upper bound for the GSV-index of a foliation
AU - Fernández-Pérez, Arturo
AU - García Barroso, Evelia R.
AU - Saravia-Molina, Nancy
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2025.
PY - 2025/4
Y1 - 2025/4
N2 - Let F be a holomorphic foliation at p∈C2, and let B be a separatrix of F. We prove the following upper bound GSVp(F,B)≤4τp(F,B)-3μp(F,B), where GSVp(F,B) is the Gómez-Mont-Seade-Verjovsky index of the foliation F with respect to B, μp(F,B) is the multiplicity of F along B and τp(F,B) is the dimension of the quotient of C{x,y} by the ideal generated by the components of any 1-form defining F and any equation of B.
AB - Let F be a holomorphic foliation at p∈C2, and let B be a separatrix of F. We prove the following upper bound GSVp(F,B)≤4τp(F,B)-3μp(F,B), where GSVp(F,B) is the Gómez-Mont-Seade-Verjovsky index of the foliation F with respect to B, μp(F,B) is the multiplicity of F along B and τp(F,B) is the dimension of the quotient of C{x,y} by the ideal generated by the components of any 1-form defining F and any equation of B.
KW - Gómez-Mont-Seade-Verjovsky index
KW - Holomorphic foliations
KW - Multiplicity of a foliation along a divisor of separatrices
KW - Tjurina number
UR - http://www.scopus.com/inward/record.url?scp=105000545163&partnerID=8YFLogxK
U2 - 10.1007/s12215-025-01215-7
DO - 10.1007/s12215-025-01215-7
M3 - Article
AN - SCOPUS:105000545163
SN - 0009-725X
VL - 74
JO - Rendiconti del Circolo Matematico di Palermo
JF - Rendiconti del Circolo Matematico di Palermo
IS - 3
M1 - 95
ER -