On the Positivity of the Products of Positive Primitive Forms

Abstract

We study the positivity of the product of two positive primitive n-forms whose restrictions to every Lagrangian subspace are nonzero. We prove that in dimensions at most six, the positivity of the product is guaranteed, while in higher dimensions, counterexamples are constructed. This answers Question 2.11 in [1]. The main content of the proof is generated by ChatGPT 5.6 and verified by the author.