cone of curves について

Words near each other

Dictionary Lists

mini英和辞書

翻訳と辞書　辞書検索 [ 開発暫定版 ]

スポンサードリンク

cone of curves ：ウィキペディア英語版

cone of curves
In mathematics, the cone of curves (sometimes the Kleiman-Mori cone) of an algebraic variety

X

X

.
==Definition==
Let

X

be a proper variety. By definition, a (real) ''1-cycle'' on

X

C=\sum a_iC_i

of irreducible, reduced and proper curves

C_i

, with coefficients

a_i \in \mathbb

. ''Numerical equivalence'' of 1-cycles is defined by intersections: two 1-cycles

C

and

C'

are numerically equivalent if

C \cdot D = C' \cdot D

for every Cartier divisor

D

X

. Denote the real vector space of 1-cycles modulo numerical equivalence by

N_1(X)

.
We define the ''cone of curves'' of

X

to be
:

NE(X) = \left\

where the

C_i

are irreducible, reduced, proper curves on

X

, and

()

their classes in

N_1(X)

. It is not difficult to see that

NE(X)

is indeed a convex cone in the sense of convex geometry.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
■ウィキペディアで「cone of curves」の詳細全文を読む

スポンサードリンク

翻訳と辞書 : 翻訳のためのインターネットリソース