Non-splitting of prime divisors
1988 ◽
Vol 103
(2)
◽
pp. 251-256
◽
Keyword(s):
Blow Up
◽
In this study of complete, or integrally closed, ideals in a two-dimensional regular local ring (R, m), Zariski established a one-to-one correspondence between prime divisors of R, i.e. rank 1 discrete valuations v birationally dominating R with residue field of transcendence degree 1 over R/m, and m-primary simple complete ideals Iv in R; cf. [17] and [18]. In this correspondence, the blow-up of such an ideal has unique exceptional prime and the localization at this prime is the valuation ring of a prime divisor of R. In this paper, we will study such ideals in a more general setting, so we begin by recalling some definitions and background results.
2003 ◽
Vol 10
(4)
◽
pp. 423-434
◽
Keyword(s):
1980 ◽
Vol 91
(2)
◽
pp. 445-456
◽
2013 ◽
Vol 13
(03)
◽
pp. 1350115
2019 ◽
Vol 19
(04)
◽
pp. 2050061
Keyword(s):
1997 ◽
Vol 27
(4)
◽
pp. 1065-1073
◽
2014 ◽
Vol 150
(10)
◽
pp. 1729-1741
◽