## Journal of Commutative Algebra

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

### 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 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

**Source**

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

**Dates**

First available in Project Euclid: 14 December 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jca/1450102159

**Digital Object Identifier**

doi:10.1216/JCA-2015-7-3-353

**Mathematical Reviews number (MathSciNet)**

MR3433986

**Zentralblatt MATH identifier**

1341.14002

**Subjects**

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

#### Citation

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. https://projecteuclid.org/euclid.jca/1450102159