On the Positivity of the Products of Positive Primitive Forms

Yuhang Liu

On the Positivity of the Products of Positive Primitive Forms

Yuhang Liu

Research output: Contribution to journal › Article

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.

Original language	English
Journal	arXiv
Publication status	Submitted - Aug 2026

Keywords

symplectic vector space
primitive form
Lagrangian subspace

Access to Document

http://arxiv.org/abs/2608.14862Licence: Unspecified

Cite this

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title = "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.",

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AB - 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.

KW - symplectic vector space

KW - primitive form

KW - Lagrangian subspace

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