【注：下文是单位群邮件的内容，标题是后加的。】

本期开始加开窗口，推出科学网特色博主，有用链接等。

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（保留若干神秘博主）

...高度一般化的方式和研究具体问题结合起来* 。

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（接2.14*）2.14. From bound on lc thresholds to boundedness of varieties. The following result connects lc thresholds and boundedness of Fano varieties, and it is one of the main ingredients of the proof of Theorem 1.1.

注：温习两周后回到出发点。做卡片，浓缩记忆。

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Theorem 2.15 ([3, Proposition 7.13]). Let d, m, v be natural numbers and let tl be a sequence of positive real numbers. Let P be the set of projective varieties X such that

• X is a klt weak Fano variety of dimension d,

• Kx has an m-complement,

• |-m Kx| defines a birational map,

• vol(-Kx)<= v, and

• for any l ∈ N and any L ∈ |-lKx|, the pair (X, tlL) is klt.

Then, P is a bounded family.

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评论：看不出 lc thresholds 及其界的痕迹。（蕴含在第四项的可能性大）。

注：此定理后面跟了一段说明，即 Th2.10, 2.11, 2.13 显示 2.15的前四项假定都对 X 满足如1.1；定理 1.4 显示第五项假定也是满足的。

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特评：没什么感觉，放几个链接吧。

1. Birational geometry...the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles.

2. Rational function...any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K. 

3. Pythagorean triple...consists of three positive integers a, b, and c, such that a² + b² = c²...The oldest known record comes from Plimpton 322...discovered by Edgar James Banks shortly after 1900, and sold to George Arthur Plimpton in 1922, for $10.

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大话：weak Fano 要求 -(Kx + B) 是 “nef and big”，不妨缩写为“nb” （简记“牛逼”）。

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小结：忘性太大。或许应该转向做卡片。这就产生一个问题：何为理解？输入并记得足够多的片段、关系，彼此能够相互解释，形成整体图像/观念。这是第一个层面，即初步理解。第二个层面该涉及规律，即联系度规和不变量，追求“自然而然”。第三个层面，即深度理解，该联系到“高观点”。（记忆是理解的必要条件，而理解可以加深或固化记忆）。对于定理，须深入理解其证明。

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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（保留若干神秘博主）