Foliations on Projective Complete Intersection K3 Surfaces

TL;DR

This paper investigates foliations on projective complete intersection K3 surfaces, focusing on when such foliations are uniquely determined by their singular schemes, and computes specific degree values related to this property.

Contribution

It characterizes degrees of foliations on K3 surfaces for which the foliation is uniquely determined by its singular scheme, extending understanding of foliation behavior on these surfaces.

Findings

Identifies degrees where foliations are uniquely determined by singular schemes

Provides explicit degree values for such foliations on K3 surfaces

Enhances classification of foliations on algebraic surfaces

Abstract

We study foliations $\mathscr{F}$ on projective complete intersection K3 surfaces $X \hookrightarrow \mathbb{P}^n$, where $\mathscr{F}$ has isolated singularities and it is the restriction of a foliation of degree $d$ on $\mathbb{P}^n$ that leaves $X$ invariant. We compute the values of the degrees $d$ for which $\mathscr{F}$ is uniquely determined by its singular scheme.