Inequalities and enumerative formulas for flags of Pfaff systems

2024/01/30 by Peña, Miguel Rodríguez, Lourenço, Fernando
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.17208

Abstract

In this work, we study inequalities and enumerative formulas for flags of Pfaff systems on ℙⁿ_ℂ. More specifically, we find the number of independent Pfaff systems that leave invariant a one-dimensional holomorphic foliation and deduce inequalities relating the degrees in the flags, which can be interpreted as the Poincaré problem for flags. Moreover, restricting to a flag of specific holomorphic foliations/distributions, we obtain inequalities involving the degrees. As a consequence, we prove stability results for the tangent sheaf of some rank two holomorphic foliations/distributions.

Related

• Analytic varieties invariant by foliations and Pfaff systems
• Bounding solutions of Pfaff equations
• Baum-Bott residue of flags of holomorphic distributions
• Degree of the Exceptional Component of the Space of Holomorphic Foliations of Degree Two and Codimension One in P3
• Degree of the exceptional component of foliations in P3