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arXiv · 1909.06714

An algorithm for a Massey triple product of a smooth projective plane curve

Younggi Lee·Jeehoon Park·Junyeong Park·Jaehyun Yim
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Abstract

We provide an explicit algorithm to compute a Massey triple product relative to a defining system for a smooth projective plane curve $X$ defined by a homogeneous polynomial $G(\underline x)$ over a field. The main idea is to use the description (due to Carlson and Griffiths) of the cup product for $H^1(X,\mathbb{C})$ in terms of the multiplications inside the Jacobian ring of $G(\underline x)$ and the Cech-deRham complex of $X$. Our algorithm gives a criterion whether a Massey triple product vanishes or not in $H^2(X)$ under a particular non-trivial defining system of the Massey triple product and thus can be viewed as a generalization of the vanishing criterion of the cup product in $H^2(X)$ of Carlson and Griffiths. Based on our algorithm, we provide explicit numerical examples by running the computer program.

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Younggi Lee, Jeehoon Park, Junyeong Park, Jaehyun Yim. 2019-09-15. An algorithm for a Massey triple product of a smooth projective plane curve. https://arxiv.org/abs/1909.06714

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