Fri, March 24, 2017
Public Access Category: All |
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- Time:
- 3:30pm-5:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: A new proof of Zariski's Theorem about Complete ideals in two-dimensional regular local rings.
Abstract: Zariski's first paper in algebra written in 1938 proved among many other results that product
of complete ideals is complete in the polynomial ring $K[X,Y]$ where $K$ is an algebraically
closed field of characteristic zero. This was generalised to two-dimensional regular local rings
in Appendix 5 of Zariski-Samuel's classic "Commutative Algebra". We will present a new proof
of this theorem using a formula of Hoskin-Deligne about co-length of a zero-dimensional
complete ideal in a two-dimensional regular local ring in terms of quadratic transforms of
$R$ birationally dominating $R.$