MONOMIAL PRINCIPALIZATION IN THE SINGULAR SETTING

Abstract. We generalize an algorithm by Goward for principalization of monomial ideals in nonsingular varieties to work on any scheme of finite type over a field. The normal crossings condition considered by Goward is weakened to the condition that components of the generating divisors meet as complete intersections. This leads to a substantial generalization of the notion of mono-mial scheme; we call the resulting schemes ‘c.i. monomial’. We prove that c.i. monomial schemes in arbitrarily singular varieties can be principalized by a sequence of blow-ups at codimension 2 c.i. monomial centers. 1