Webs Generated by Products of convex and homogeneous Foliations on $\mathbb{P}^2$

TL;DR

This paper introduces methods for constructing flat webs on the projective plane by combining convex foliations and invariant lines, demonstrating their dual webs are flat.

Contribution

It presents two novel methods for constructing flat webs using convex and homogeneous foliations, expanding the understanding of web geometry on projective planes.

Findings

Product of convex reduced foliations yields flat dual webs.

Product of convex homogeneous foliations yields flat dual webs.

Methods provide new tools for web construction in algebraic geometry.

Abstract

This paper investigates flat webs on the projective plane. We present two methods for constructing such webs: the first involves taking the product of finitely many convex reduced foliations and invariant lines, while the second consists of taking the product of finitely many convex homogeneous foliations and invariant lines. In both cases, we demonstrate that the dual web is flat.