Deformations of pullback foliations

2024/12/28 by Perrella, Pablo
#14D15 #32M25 #32S65 #37F75 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.19968

Abstract

We study the stability of pullback foliations under morphisms and rational maps via Grothendieck's Drapeaux scheme. In the local setting, a foliated version of Schlessinger's Theorem on rigidity of conical singularities was achieved. We apply these techniques to provide a criterion for the stability of algebraic leaves of a foliation.

Related

• Stability of branched pull-back projective foliations
• Stability of pullbacks of foliations on weighted projective spaces
• Branched pull-back components of the space of codimension 1 foliations on \mathbb Pⁿ
• Schlesinger foliation for deformations of foliations
• Rational pullbacks of toric foliations