The simplest minimal free resolutions in P1×P1,

N. BOTBOL, A. DICKENSTEIN, H. SCHENCK

Commutative Algebra II

Springer

Año: 2021; p. 113 - 145

We study the minimal bigraded free resolutionof an ideal with three generators of the same bidegree, contained in thebihomogeneous maximal ideal ⟨s,t⟩∩⟨u,v⟩ of the bigraded ring K[s,t;u,v]. Ouranalysis involves tools from algebraic geometry (Segre-Veronese varieties),classical commutative algebra (Buchsbaum-Eisenbud criteria for exactness,Hilbert-Burch theorem), and homological algebra (Koszul homology, spectralsequences). We treat in detail the case in which the bidegree is (1,n). Weconnect our work to a conjecture of Fröberg-Lundqvist on bigraded Hilbertfunctions, and close with a number of open problems.