LE TISSU DUAL D’UN PRÉ-FEUILLETAGE CONVEXE RÉDUIT SUR P2C EST PLAT

The paper proves that the dual d-web of any reduced convex pre-foliation F = C ⊠ 𝔽 on P^2 is flat via: (i) a discriminant formula for LegF, (ii) local decompositions of LegF along each irreducible discriminant component, (iii) a curvature “reduction” criterion for totally invariant components of minimal multiplicity, and (iv) a global vanishing argument on P^2. The candidate solution follows the same structure and uses the same ingredients (discriminant description, local splittings near dual lines and along C^∨, holomorphy criterion, and the absence of holomorphic 2-forms on P^2^∨) to conclude flatness. Minor wording differences aside, they are effectively the same proof, and both are correct. Key steps and statements are explicitly present in the paper: main theorem (Théorème 1) and its roadmap, the discriminant formula (Lemme 3.1, (3.4) and Corollaire 3.2), the two local splittings (Lemmes 5.1 and 5.3), the reduction criterion (Proposition 6.2), the curvature characterization on P^2, and the final global vanishing in the proof of Théorème 1 (using K_{P^2} of degree −3) .