三维Demailly-Semple射流研究

二维空间中4阶和5阶Demailly-Semple喷流

Demailly-Semple jets of orders 4 and 5 in dimension 2

基于Kobayashi的双曲性猜想，本文研究了二维4阶和5阶Demailly-Semple喷注，通过系统的、大量的、形式化的、手工的计算，证明了它们的代数驯服性.

On the Demailly-Semple jet bundles of hypersurfaces in $\CP^3$

Let $X$ be a smooth hypersurface of degree $d$ in $\CP^3$. By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle $X_3$ of $X$, the bundle $\ocal_{X_3}(1)$ is big for $d\geq 11$, and that on the fourth Demailly-Semple jet bundle $X_4$ of $X$, the bundle $\ocal_{X_4}(1)$ is big for $d\geq 10$, improving a recent result of Diverio.

广义Demaily-Semple喷丛与复流形的全纯映射

Generalized Demailly-Semple jet bundles and holomorphic mappings into complex manifolds

受Green-Griffiths猜想的启发，我们研究了从$\C^p$到复流形的极大秩全纯映射.当使用$p>1$时，原则上这些图应该比整个曲线更易处理。我们扩展到这个设置的喷射束技术介绍了森普尔，绿色格里菲斯和Demailly。我们的主要应用是证明了从$\C^2$到$\bP^4$中非常一般次数的$d$超曲面的极大秩全纯映射的不存在性，只要$d\geq 93.$

On the structure of Demailly-Semple invariant jet differentials

A short explanation of the complexity of the structure of Demailly-semple invariant jet differentials was given

Structural Invariance of Green--Griffiths--Demailly Thresholds on Compact Complex Orbifolds

We prove that the Green--Griffiths--Demailly (GGD) hyperbolicity thresholds are structurally invariant. In other words, the minimal jet order and asymptotic growth rate at which invariant jet differentials appear remain unchanged when passing from a compact complex manifold to any compact smooth analytic Deligne--Mumford stack (orbifold) with the same coarse Kähler class. We establish an orbifold Riemann--Roch formula showing that only the identity sector contributes to the leading $m^n$ term of the Euler characteristic $χ$, while all twisted sectors contribute only $O(m^{n-1})$. Together with…

Applications of computational invariant theory to Kobayashi hyperbolicity and to Green-Griffiths algebraic degeneracy

A major unsolved problem (according to Demailly 1997) towards the Kobayashi hyperbolicity conjecture in optimal degree is to understand jet differentials of germs of holomorphic discs that are invariant under any reparametrization of the source. The underlying group action is not reductive, but we provide a complete algorithm to generate all invariants, in arbitrary dimension n and for jets of arbitrary order k. Two main new situations are studied in great details. For jets of order 4 in dimension 4, we establish that the algebra of Demailly-Semple invariants is generated by 2835 polynomials, …