轴心之问,用猜的办法来学习全新概念

来源:http://www.roro2.com 作者:必威betway 人气:158 发布时间:2019-08-24
摘要:This is an in-mail fromTYUST. 评论:总之,给定条件E = Supp,则(X,Supp 入格 ==(W,Θw Aw) 入格. ---- 暂时假设 closed point 以外 klt 相当于 0-lc. 本期开始分组发送邮件,搭载数学类学院等链接。 注:

This is an in-mail fromTYUST.

评论:总之,给定条件E = Supp,则(X,Supp 入格 ==>(W,Θw Aw) 入格.

---- 暂时假设 closed point 以外 klt 相当于 0-lc.

本期开始分组发送邮件,搭载数学类学院等链接。必威betway 1

注:1, 2 是替换操作; 3, 4 是就替换后而言.

本期开始分组发送邮件,搭载数学类学院等链接。必威betway 2

---- 这里引用了定理1.6 (假定维度≤ d - 1).

(接前:292625) 命题5.7的证明.

(此处“通”指 a(T, W, E = 0; “盘”指 a≤1).

---- 构造出有界族配对 (X, Supp. 图解:

In particular,(X, B tB)is eps/2-lc outside these finitely many closed points because Kx B tB = 1/2 1/2(Kx B 2tB).

---- 上一句提及的一大堆丰量后文似乎并未用到.

本期开始分组发送邮件,搭载数学类学院等链接。必威betway 3

(接前:242221) 命题5.7的证明.

---- 这里涉及到 “closed point”,但出处不详.

今日学院:暂无。||新闻 ||符号大全、上下标.|| 常用:↑↓ π ΓΔΛΘΩμφΣ∈∉∪ ∩⊆ ⊇ ⊂ ⊃≤ ≥⌊ ⌋⌈ ⌉≠⁻⁰¹ ² ³ᵈ₀ ₁₂₃ᵢₐ.

Step3.(B 和 L 进入“戏份”).

---- 原作引入的记号Θw 会让人忍不住问:Θ 是什么角色?(带上下标w,也许只是为了提示与 W的联系?).

小结:Step4 第一段读写完毕.

In particular, Aw - Bw is ample, hence Aw - Δw = α is ample too.

  1. 是 δ-lc 型..

  2. a = 0 ==> a≤1.

  1. 乘法: degAΛ = Aᵈ⁻¹Λ≤Aᵈ≤r.

  2. 加法: Supp.

Glossary

Abstract8/4

Introduction

Boundedness of singular Fano varieties 8/5

Boundedness of singular Fano varieties 8/6

Boundedness ofsingularFano varieties 8/7

Boundedness ofsingularFano varieties 8/8

Boundedness ofsingularFanovarieties 8/9

Boundedness ofsingularFanovarieties8/9

Jordan property of Cremona groups8/10

Lc thresholds of lR-linear systems 8/11

Lc thresholds of anti-log canonical systems of Fano pairs 8/12

Lc thresholds of anti-log canonical systems of Fano pairs 8/13

Lc thresholds of R-linear systems with bounded degree 8/14

Complements near a divisor8/15

Proposition 5.211/9

Proposition 5.511/5

Leonhard EulerCarl Friedrich GaussGrothendieck

(α只依赖于P,Q.)

Replace A with a general member of |A|.

Since we are assuming Theorem 1.6 in dimension≤d - 1, by taking hyperplane sections, we find a positive number t depending only on d, r, eps such that (X, B 2tB) is klt outside finitely many closed points.

---- Step3的真正轴心在这里!

  1. 是 sub-eps-lc 型.

  2. 是 lc 型.

This is an in-mail fromTYUST.

今日学院:暂无。||符号大全、上下标.|| 常用:↑↓ π ΓΔΛΘΩμφΣ∈∉∪ ∩⊆ ⊇ ⊂ ⊃≤ ≥⌊ ⌋⌈ ⌉≠⁻⁰¹ ² ³ᵈ₀ ₁₂₃ᵢₐ.

On the other hand, we can chooseφ: W --> X and Aw so thatAw -Θw,1/2Aw

  1. eps <- δ, P <- Q, r <-*

  2. {X, B, A, L,Λ, x} <- {W, Δw, Aw, Lw, E, ω}.

  3. 是 log smooth 型 .

  4. 仍假定 x 闭合.

----(X,Supp 入格 ==>

All the assumptions of Proposition 5.5 are satisfied in our setting except that SuppB may contain some strata of apart from x.

---- 但这里推导出它也是 ls.

(此处的lc 是全局的?)

---- 两物并立曰“方”,有“方”必有“法”. 法即映射.

新入の者-->What is going on ?(redirected)必威betway 4new

---- 难道这句话才是真正的轴心?

Leonhard EulerCarl Friedrich GaussGrothendieck

Leonhard EulerCarl Friedrich GaussGrothendieck

---- 现在只剩SuppB 与 stratum 的关系问题.

人是精神的存在。

小结:Step3 温习完毕.

---- degAΛ≤r预示相合乎法度.

This is an in-mail fromTYUST.

This is an in-mail fromTYUST.

组阁·丰之战·大换届.



---- 怎么选择?或为何能选择?

  1. 取 Kx B 的回拉 Kw Bw.

  2. Bw 的系数有下界.

  3. 写出 Kw Jw =φ*Kx, 其中 Jw≤Bw.

  4. Jw 的系数有下界.

  5. 有α∈ 使Δw:=αBw ≥ 0.

---- nΛ 为整系数.

---- 此句表明,整个证明是向命题5.5的条件靠拢.

小结:Step3 读写完毕.

(接前:110908)温习:命题5.7的证明.

新入の者-->What is going on ?(redirected)必威betway 5new

---- 这里出现另一配对 (X, B tB).

新入の者-->What is going on ?(redirected)必威betway 6new

  1. Aw - E 丰.

  2. 1/2Aw Kw 丰.

  3. 1/2Aw - 丰.

  4. Aw - Lw 丰.

  5. Aw - Bw 丰.

  6. Aw - Δw = α 丰.

----φ的exceptional divisors 求和,我宁愿记作 E.

本期开始分组发送邮件,搭载数学类学院等链接。必威betway 7

---- 能选择φ和Aw使得一大堆量 ample.

注:1 ==> 2,3,4,5; 3,4 ==> 6; 2, 6 ==> 7.

Step2 第一段 .

---- 没有出现矛盾,前述假设成立.

Now after replacing eps with δ, replacingPwithQ, and replacing r approriately, we can replace X, B, A, L,Λ, x with W,Δw, Aw, Lw,Θw, ω, respectively.

(像不像一场 “丰之战” ?)

---- 局部 lc .

Step4. 第一段 .

  • Kw, 1/2Aw - , and Aw - Lw are all ampe where Lw is the pullback of L.

---- 此举的用意暂不清楚.

---- 但定理1.6没有直接出现这里的结果.

Note that we can assume x is still a closed point, by Step 1.

新入の者-->What is going on ?(redirected)必威betway 8new

---- 对其exceptional divisors 求和,记作Θw.

---- 注意,这里出现新的配对(X, B 2tB).

---- we can assume...

Glossary

必威betway,Abstract8/4

Introduction

Boundedness of singular Fano varieties 8/5

Boundedness of singular Fano varieties 8/6

Boundedness ofsingularFano varieties 8/7

Boundedness ofsingularFano varieties 8/8

Boundedness ofsingularFanovarieties 8/9

Boundedness ofsingularFanovarieties8/9

Jordan property of Cremona groups8/10

Lc thresholds of lR-linear systems 8/11

Lc thresholds of anti-log canonical systems of Fano pairs 8/12

Lc thresholds of anti-log canonical systems of Fano pairs 8/13

Lc thresholds of R-linear systems with bounded degree 8/14

Complements near a divisor8/15

Proposition 5.211/9

Proposition 5.511/5

Glossary

Abstract8/4

Introduction

Boundedness of singular Fano varieties 8/5

Boundedness of singular Fano varieties 8/6

Boundedness ofsingularFano varieties 8/7

Boundedness ofsingularFano varieties 8/8

Boundedness ofsingularFanovarieties 8/9

Boundedness ofsingularFanovarieties8/9

Jordan property of Cremona groups8/10

Lc thresholds of lR-linear systems 8/11

Lc thresholds of anti-log canonical systems of Fano pairs 8/12

Lc thresholds of anti-log canonical systems of Fano pairs 8/13

Lc thresholds of R-linear systems with bounded degree 8/14

Complements near a divisor8/15

.Proposition 5.211/9

Proposition 5.5. 11/5

----后文整个围绕这件事展开.

---- 丰量的凸组合仍为丰量.

评论:Bw 与 E “联袂”,引出轴心配对, “通盘”.

评论:方成于法,法现于方。法在对角,“出新”。

We will modify B so that this assumption on support of B is also satisfied.

Glossary

Abstract8/4

Introduction

Boundedness of singular Fano varieties 8/5

Boundedness of singular Fano varieties 8/6

Boundedness ofsingularFano varieties 8/7

Boundedness ofsingularFano varieties 8/8

Boundedness ofsingularFanovarieties 8/9

Boundedness ofsingularFanovarieties8/9

Jordan property of Cremona groups8/10

Lc thresholds of lR-linear systems 8/11

Lc thresholds of anti-log canonical systems of Fano pairs 8/12

Lc thresholds of anti-log canonical systems of Fano pairs 8/13

Lc thresholds of R-linear systems with bounded degree 8/14

Complements near a divisor8/15

.Proposition 5.211/9

Proposition 5.5. 11/5

今日学院:暂无。||符号大全、上下标.|| 常用:↑↓νπ ΓΔΛΘΩμφΣ∈∉∪ ∩⊆ ⊇ ⊂ ⊃≤ ≥⌊ ⌋⌈ ⌉≠⁻⁰¹ ² ³ᵈ₀ ₁₂₃ᵢₐ.

Since nΛis integral and degAΛ< Aᵈ≤r, the pair (X, Supp belongs to a bounded family of pairsPdepending only on d, r, n.

---- 将修改 B 使之满足“禁”的条件.

Step3. 第二段 .

注:以上,1; 3,4==>2 ==> 5; 6,7==>8; 9.

---- 对角线上有两个运算:

(接前:302926) 命题5.7的证明.

---- 条件中的 是 “局部 lc”.

Thus there exist a log resolutionφ: W --> X of and a very ample divisor Aw≥0 so that if Θw is the sum of the exceptional divisors ofφand the support of the birational transform ofΛ, then (W,Θw Aw) belongs to a bounded familyQof pairs depending only on d, r, n,P.

Leonhard EulerCarl Friedrich GaussGrothendieck

Step3. 第三段.

---- 即E =Θw =Supp.

---- 它是 和 (X, B 2tB) 的凸组合.

In particular, is log smooth withΛreduced.

今日学院:暂无。||新闻 ||符号大全、上下标.|| 常用:↑↓ π ΓΔΛΘΩμφΣ∈∉∪ ∩⊆ ⊇ ⊂ ⊃≤ ≥⌊ ⌋⌈ ⌉≠⁻⁰¹ ² ³ᵈ₀ ₁₂₃ᵢₐ.

---- 由此,1/2eps 1/2·0 = 1/2eps (参 Lemma 2.3).

---- 若Θw = Supp, 则(W,Θw Aw) 入格.

用猜的办法来学习全新概念.

----φ是回拉式,着意于 W 空间.

---- (X,Supp 属于有界族,即“入格”.

----Supp 预示侯相联合,“摄领相事”.

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