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Monomial principalization in the singular setting

2013/10/04 by Corey Harris, Harris, Corey
Mathematics · #14B05 (Primary) 14C17 #14M10 #14Q99 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14B05 #msc:14C17 #msc:14M10 #msc:14Q99

paper · pdf · doi:10.48550/arxiv.1310.1261

7 pages, 2 figures

arxiv created 2014/04/15 · arxiv updated 2014/04/16

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 `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.

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