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# Computing residue currents of monomial ideals using comparison formulas

Övrigt
Författare Richard Lärkäng Elizabeth Wulcan 2012 Institutionen för matematiska vetenskaper, matematik en arxiv.org/abs/1205.4648 arxiv.org/pdf/1205.4648v1 Algebra och geometri, Matematisk analys

## Sammanfattning

Given a free resolution of an ideal \$\mathfrak{a}\$ of holomorphic functions, one can construct a vector-valued residue current, \$R\$, which coincides with the classical Coleff-Herrera product if \$\mathfrak{a}\$ is a complete intersection ideal and whose annihilator ideal is precisely \$\mathfrak{a}\$. We give a complete description of \$R\$ in the case when \$\mathfrak{a}\$ is an Artinian monomial ideal and the resolution is the hull resolution (or a more general cellular resolution), extending previous results by the second author. The main ingredient in the proof is a comparison formula for residue currents due to the first author.