Let J be the product of n ideals generated by linear forms in a polynomial ring. We describe a minimal free resolution of J and show that it is supported on a polymatroid obtained from the underlying representable polymatroid by means of the so-called Dilworth truncation. Formulas for the projective dimension and Betti numbers are given in terms of the polymatroid as well as a characterization of the associated primes.
Resolution of ideals associated to subspace arrangements
Aldo,Conca;Manolis,Tsakiris
2022-01-01
Abstract
Let J be the product of n ideals generated by linear forms in a polynomial ring. We describe a minimal free resolution of J and show that it is supported on a polymatroid obtained from the underlying representable polymatroid by means of the so-called Dilworth truncation. Formulas for the projective dimension and Betti numbers are given in terms of the polymatroid as well as a characterization of the associated primes.
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(2022) Conca Tsakiris Resolution of ideals associated to subspace arrangements.pdf
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