Journal of Commutative Algebra

Monomial principalization in the singular setting

Corey Harris

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

Permanent link to this document

Digital Object Identifier

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.

Export citation


  • Paolo Aluffi, Segre classes as integrals over polytopes, J. Eur. Math. Soc., to appear.
  • David Eisenbud, Commutative algebra: With a view toward algebraic geometry, Grad. Texts Math., Springer-Verlag, New York, 1995.
  • William Fulton, Intersection theory, 2nd edition, Ergeb. Math. Grenz. 2, Springer-Verlag, Berlin, 1998.
  • Russell A. Goward, Jr., A simple algorithm for principalization of monomial ideals, Trans. Amer. Math. Soc. 357 (2005), 4805–4812 (electronic).