AI 中文总结
该研究探讨正本原n-形式乘积的正性问题，证明维数≤6时乘积正性成立，高维时存在反例，回答了文献[1]的问题2.11，证明内容由ChatGPT 5.6生成并经作者验证。
AI 中文摘要
我们研究两个正本原n-形式的乘积的正性，这两个形式在每个拉格朗日子空间上的限制均非零。我们证明，在维数不超过6时，该乘积的正性是有保证的，而在更高维数时则构造了反例。这回答了文献[1]中的问题2.11。证明的主要内容由ChatGPT 5.6生成并经作者验证。
英文摘要
Let $(V_i,ω_i)$ be real symplectic vector spaces and let $Ω_i\in\mathcal U^+(V_i)$ in the sense of Haiden. We prove that $p_1^*Ω_1\wedge p_2^*Ω_2$ belongs to $\mathcal U^+(V_1\oplus V_2)$ whenever one factor has real dimension at most six. There are forms $Ω\in\mathcal{U}^+(\mathbb{R}^6)\setminus\mathcal{U}_{\mathrm{ag}}(\mathbb{R}^6)$ for which $p_1^*Ω\wedge\cdots\wedge p_k^*Ω$ belongs to $\mathcal{U}^+$ for every $k\geq 1$; hence a conjecture of Kontsevich does not hold in complex dimension three. We also give a criterion for a product to belong to $\mathcal{U}$ and show that, for every $N\geq 26$, there are two forms in $\mathcal{U}^+(\mathbb{C}^N)$ whose exterior product does not belong to $\mathcal{U}$. The main content of this paper is generated by ChatGPT 5.6 and verified by the author.
Comments12 pages. AI Generated and human verified. Current version refined by AI. Comments are welcome
