Electronic Resource
Springer
Annali di matematica pura ed applicata
142 (1985), S. 277-292
ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary This paper is dedicated to the study of Hilbert functions and Betti numbers of the projective varieties in a flat family. We prove that the Hilbert function H(X y ,n),y ∈ Y-a parameter scheme-is lower semicontinuous for any fixed n. In case Y is integral and noetherian we obtain the well-known fact that the set V ⊂Y where H(X y ,n)is maximal for all n's is open and nonempty. We show also that bi(X y )-the i- th Betti number of Xy—is upper semicontinuous for y ∈ V. The paper contains also a number of results concerning the relations among the various Betti numbers.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01766597
Permalink
|
Location |
Call Number |
Expected |
Availability |