Blowing up monomial ideals

✍ Scribed by Marc Levine

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 294 KB
• Volume: 160
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00067-0

✦ Synopsis

Let k be a ÿeld. Spivakovsky's theorem on the solution of Hironaka's polyhedral game has been extended by Bloch to show that a morphism f : Z → S of ÿnite type k-schemes can be put in good position with respect to a normal crossing divisor @S on S by taking the proper transform with respect to an iterated blowing up of faces of @S. We extend these results to schemes of ÿnite type over a regular scheme of dimension one, including the case of mixed characteristic.