Journal of Commutative Algebra

Monomial principalization in the singular setting

Corey Harris

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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 monomial scheme; we call the resulting schemes `\textit{regular crossings} (r.c.) \textit{monomial}.' We prove that r.c.~monomial subschemes in arbitrarily singular varieties can be principalized by a sequence of blow-ups at codimension~2 r.c.~monomial centers.

Article information

J. Commut. Algebra Volume 7, Number 3 (2015), 353-362.

First available in Project Euclid: 14 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]


Harris, Corey. Monomial principalization in the singular setting. J. Commut. Algebra 7 (2015), no. 3, 353--362. doi:10.1216/JCA-2015-7-3-353.

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