论文标题
不变的喷气差异和渐近性二元性
Invariant Jet differentials and Asymptotic Serre duality
论文作者
论文摘要
我们概括了Demailly \ cite {d2}的主要结果，以捆绑$ e_ {k，m}^{gg}（gg}（v^*）$的订单$ k $的喷气差值和加权度$ m $ to bungles $ e_ e_ {k，m}（k，m}（v^*）的订单$ k $ $ k $ $ k $ $ k $ k $ k $ k $ m。也就是说，定理0.5来自\ cite {d2}和\ cite {d1}的定理9.3提供了一个下限的$ \ frac {c^k} {k} {k} m^{n+kr-1} $在线性独立的全球段的$ e _ _ { \ Mathcal {o}（-MΔA）$，用于某些足够的Divisor $ a $。 The group $G_k$ of local reparametrizations of $(\mathbb{C},0)$ acts on the $k$-jets by orbits of dimension $k$, so that there is an automatic lower bound $\frac{c^k}{k} m^{n+kr-1}$ on the number of the linearly independent holomorphic global sections of $ e_ {k，m} v^* \ bigotimes \ mathcal {o}（ - mΔa）$。我们制定并证明沿绿木束的纤维纤维上的渐近二元性在投射歧管上存在。我们还证明了喷气束的渐近切片二元性。还为部分申请申请了绿色长石的猜想。
We generalize the main result of Demailly \cite{D2} for the bundles $E_{k,m}^{GG}(V^*)$ of jet differentials of order $k$ and weighted degree $m$ to the bundles $E_{k,m}(V^*)$ of the invariant jet differentials of order $k$ and weighted degree $m$. Namely, Theorem 0.5 from \cite{D2} and Theorem 9.3 from \cite{D1} provide a lower bound $\frac{c^k}{k}m^{n+kr-1}$ on the number of the linearly independent holomorphic global sections of $E_{k,m}^{GG} V^* \bigotimes \mathcal{O}(-m δA)$ for some ample divisor $A$. The group $G_k$ of local reparametrizations of $(\mathbb{C},0)$ acts on the $k$-jets by orbits of dimension $k$, so that there is an automatic lower bound $\frac{c^k}{k} m^{n+kr-1}$ on the number of the linearly independent holomorphic global sections of $E_{k,m}V^* \bigotimes \mathcal{O}(-m δA)$. We formulate and prove the existence of an asymptotic duality along the fibers of the Green-Griffiths jet bundles over projective manifolds. We also prove a Serre duality for asymptotic sections of jet bundles. An application is also given for partial application to the Green-Griffiths conjecture.
