Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Projective normal flatness and Hilbert functions


Authors: U. Orbanz and L. Robbiano
Journal: Trans. Amer. Math. Soc. 283 (1984), 33-47
MSC: Primary 14B25; Secondary 13H15
MathSciNet review: 735407
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Projective normal flatness of a local ring $ R$ along an ideal $ I$ is defined to be the flatness of the morphism on the exceptional divisor induced by blowing up $ R$ with center $ I$. It is shown that most of the important properties of normal flatness have an analogue for projective normal flatness. In particular, we study the local Hilbert function in connection with projective normal flatness. If $ R/I$ is regular and $ R$ projectively normally flat along $ I$, then we obtain the same inequality for the local Hilbert functions under blowing up as in the permissible case.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14B25, 13H15

Retrieve articles in all journals with MSC: 14B25, 13H15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0735407-1
PII: S 0002-9947(1984)0735407-1
Keywords: Normal flatness, regular sequence, Hilbert function, blowing up, associated graded ring
Article copyright: © Copyright 1984 American Mathematical Society