这是一份介绍Kodaira-Akizuki-Nakano vanishing theorem(比Kodaira最开始的形式强一些)和Kodaira embedding theorem的笔记,只假设一点点多复变与复流形、微分几何、层与上同调的基本概念,内容除了泛函分析的几…
Rao-Blackwell Theorem:布莱克威尔定理 Picard’s Little Theorem:皮卡小定理 The Perron-Frobenius Theorem:门阶Frobenius定理 Bloch´s theorem:布洛赫定理 Duhamel´s Theorem:Duhamel定理 Prime Number Theorem - ONID素数定理- 3 The Vanishing of Sidney Hall《消失的西德尼·豪尔(2017)》完整中英文对照...
Theorem 1.4(Kodaira Vanishing Theorem): LetXbe a smooth complex projective variety of dimension n, and letAbe an ample divisor onX. Then we have Hi(X,OX(KX+A))=0,i>0 or equivalently Hj(X,OX(−A))=0,j<n=dimX Lemma 1.2: LetXbe a smooth complex projective variety of dimension ...
Fuj15a] O. Fujino, Kodaira vanishing theorem for log-canonical and semi-log-canonical pairs, Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 8, 112-117.O. Fujino, Kodaira vanishing theorem for log-canonical and semi-log-canonical pairs, Proc. Japan Acad. Ser. A Math. Sci. ...
例如,fixed compact complex manifold上holomorphic vector bundle上的complex structure,但总是在类似于𝐻^2(𝑀; 𝑇_𝑀) vanishing的假设下:a space of “obstructions” vanishes。然而,到那时,众所周知,有些例子表明,complex structure的变化不是由ℂ𝑛中的open set局部描述的(described locally),而是由...
The Kodaira Embedding Theorem is extended to Kähler varieties with isolated singularities. UsingL 2 estimates for the bundle-valued∂¯−operator, it is shown that a necessary and sufficient condition for a compact normal Kähler variety with isolated singularities to be biholomorphic to a ...
Kodaira vanishing theorem on noncomplete algebraic manifolds - Bauer, Kosarew - 1990I. Bauer, S. Kosarew: On the Hodge spectral sequences for some classes of non-complete algebraic manifolds. Math. Ann. 284 (1989), 577 - 593Kosarew, I., Kosarew, S.: Kodaira vanishing theorems on non-...
The first part is devoted to proving a singular version of the logarithmic Kodaira-Akizuki-Nakano vanishing theorem of Esnault and Viehweg. This is then used to prove other vanishing theorems. In the second part these vanishing theorems are used to prove an Arakelov-Parshin type boundedness result...
In this line we proveTheorem 7.4,Theorem 7.5. Part (1) inTheorem 7.4is new since we consider all Kodaira fibers, which includes curves that are non-reduced and even multiple curves. Part (2) provides a new proof for the result given in[24]. We no longer need to use neither the equiv...
1) Kodaira vanishing theorem Kodaira消灭定理 1. Finally ,we prove theKodaira vanishing theoremand the Hodge theorem. 本文介绍了复流形上偏微分算子v,(?),δ以及复Laplacian □,(?),△的定义,计算了偏微分算子v,口作用于C~∞(p,q)-形式后得到的新的微分形式的分量,验证了Kodaira消灭定理和Hodge定理。