Abstract
We study the minimal bigraded free resolution of an ideal with three generators of the same bidegree, contained in the bihomogeneous maximal ideal 〈s, t〉∩〈u, v〉 of the bigraded ring \(\mathbb {K}[s,t;u,v]\). Our analysis involves tools from algebraic geometry (Segre-Veronese varieties), classical commutative algebra (Buchsbaum-Eisenbud criteria for exactness, Hilbert-Burch theorem), and homological algebra (Koszul homology, spectral sequences). We treat in detail the case in which the bidegree is (1, n). We connect our work to a conjecture of Fröberg–Lundqvist on bigraded Hilbert functions, and close with a number of open problems.
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