本期开始加开窗口，推出科学网特色博主，有用链接等。

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他将自己的创造力归因于...一个孩子的天真而热情的好奇心*。

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（接上回*）Proof. (of Corollary 1.2) Since Δ is big, Δ ~R A + D where A is ample and D ≥ 0. Thus there is α ∈ (0, 1) such that if we let

 Γ =(1 - α) Δ + α D, 

then (X, Γ) is ε/2 - lc and -(Kx + Δ) is ample. Now apply Theorem 1.1.

评论：证明含有4个推导，看上去并不显然。（换句话说：看不懂）。

跳点：

1. 推论1.2的表述; （做卡片）

2. “big” 的含义；

3. “ample”的含义；

温习：

推论1.2的表述：{Xp} 有界，若 (X, Δ) 是 “eps-lc 零扩副大边”。

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小结：看上去该了解点基本概念了...现在就开始！（见如下外网摘录）

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A line bundle on a projective variety is ample if some tensor power of it is very ample.（链接）.

An ample line bundle is one such that some positive power is very ample.（链接）.

A line bundle L on a variety X is very ample if X can be embedded into a projective space so that L is the restriction of Serre's twisting sheaf O(1) on the projective space.

a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold  into projective space. 

评论：两个基本概念“ample”和“very ample”，用于描述“line bundle”的性质。看上去“very ample”更为基本。

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A big line bundle L on X of dimension n is a line bundle such that .（链接）

A line bundle is big if it is of maximal Iitaka dimension, that is, if its Iitaka dimension is equal to the dimension of the underlying variety. Bigness is a birational invariant: If f : Y → X is a birational morphism of varieties, and if L is a big line bundle on X, then f^*L is a big line bundle on Y. （链接）

All ample line bundles are big.

Big line bundles need not determine birational isomorphisms of X with its image. For example, if C is a hyperelliptic curve (such as a curve of genus two), then its canonical bundle is big, but the rational map it determines is not a birational isomorphism. Instead, it is a two-to-one cover of the canonical curve of C, which is a rational normal curve.

评论：“big”也是用来描述“line bundle”的性质。

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a line bundle on a complete algebraic variety over a field is said to be nef if the degree of its restriction to every algebraic curve in the variety is non-negative. The term "nef" was introduced by Miles Reid^[1] as a replacement for the older terms "arithmetically effective" (Zariski 1962, definition 7.6) and "numerically effective", as well as for the phrase "numerically eventually free".  (A line bundle is called semi-ample or "eventually free" if some positive power is basepoint-free.) （链接）

Every semi-ample divisor is nef, but not every nef divisor is numerically equivalent to a semi-ample divisor, or even to an effective divisor.

评论：“nef”仍然是“line bundle”的性质。

今日博主：徐令予李颖业张忆文林中祥 张云李学宽武夷山 宁利中蒋迅蒲亨建 刘全慧 谢力Grothendieck 韩健 毛宏王庆浩尤明庆张操曾新林文克玲蔡宁吕洪波杨正瓴彭真明蒋继平姬扬徐耀刘钢刘全生吕喆 王鸿飞 马臻 刘进平 赵美娣 鲍永利 戴世强 周涛 刘洋 邢志忠 曾泳春郭景涛郑永军（保留若干神秘博主）