||
[注:下文作为笔记的附件,为方便温习及简化笔记的结构。]
.
It's going on here for the third round of learning of Birkar's BAB-paper (v2), with scenarios of chess stories. No profession implications.
Sub-pairs are classified by introducing the concept of "log discrepancy" which is defined as
a(D, X, B): = 1 - [Bw]
where [·] takes the coefficient of Bw on D, a prescribed prime divisor; Bw is the image of B in W resulted from the map called "log resolution"
φ: W --> X
with respect to the sub-pair (X, B).
Note: [Bw] is a homemade notation for μDBW, the coefficient of Bw on D.
.
Three typical types/ states of a sub-pair ——
.
. sub-lc, a ≥ 0
(X, B) is sub-klt, if a > 0 holds for every D.
sub-eps-lc, a ≥ eps
.
It is possible for a log discrepancy to take a non-positive value. Consider a prime divisor D on birational models of X. One call D a non-klt place of (X, B), if a ≤ 0. The image on X of a non-klt place is called non-klt centre. Note that, "non-klt" is replaced by "lc" for lc pairs in some texts, to say lc-place or lc centre. [Nov. 21]
Archiver|手机版|科学网 ( 京ICP备07017567号-12 )
GMT+8, 2024-9-26 06:49
Powered by ScienceNet.cn
Copyright © 2007- 中国科学报社