2019/09/15 by Lee, Younggi, Park, Jeehoon, Park, Junyeong +1
#13D10 (secondary) #14D15 #14J70 #18G55(primary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1909.06714
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 H1(X,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 H2(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 H2(X) of Carlson and Griffiths. Based on our algorithm, we provide explicit numerical examples by running the computer program.