Open Access
FALL 2015 Monomial principalization in the singular setting
Corey Harris
J. Commut. Algebra 7(3): 353-362 (FALL 2015). DOI: 10.1216/JCA-2015-7-3-353


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.


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Corey Harris. "Monomial principalization in the singular setting." J. Commut. Algebra 7 (3) 353 - 362, FALL 2015.


Published: FALL 2015
First available in Project Euclid: 14 December 2015

zbMATH: 1341.14002
MathSciNet: MR3433986
Digital Object Identifier: 10.1216/JCA-2015-7-3-353

Primary: 14B05

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

Vol.7 • No. 3 • FALL 2015
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