论文标题
投影空间产物中非常普遍的曲面的代数双曲线
Algebraic hyperbolicity of very general hypersurfaces in products of projective spaces
论文作者
论文摘要
我们通过使用EIN，Voisin，Pacienza，Coskun和Riedl和其他的三种技术来研究$ \ Mathbb {p}^M \ times \ Mathbb {p}^n $中非常普遍的超曲面的代数双曲线。结果，我们完全回答了一个问题，即在$ \ Mathbb {p}^m \ times \ times \ mathbb {p}^n $中是否非常普遍的低表情（a，b）$（a，b）$是代数是多余的（7,3），（6,3）$和$（5，b）$，带有$ b \ geq 3. $作为这些技术的另一种应用，我们改善了已知的结果，即在$ \ mathbb {p}^n $ a a $ 2n-2 $中至少是$ n \ n $ n \ geq 6 $ n = $ n = 4 $ n = 4 $ n = 4 $ n = 4 $ n = 4 $ n = $ 2n-2 $的非常普遍的hypersurfaces，至少是$ 2n-2 $。
We study the algebraic hyperbolicity of very general hypersurfaces in $\mathbb{P}^m \times \mathbb{P}^n$ by using three techniques that build on past work by Ein, Voisin, Pacienza, Coskun and Riedl, and others. As a result, we completely answer the question of whether or not a very general hypersurface of bidegree $(a,b)$ in $\mathbb{P}^m \times \mathbb{P}^n$ is algebraically hyperbolic, except in $\mathbb{P}^3 \times \mathbb{P}^1$ for the bidegrees $(a,b)= (7,3), (6,3)$ and $(5,b)$ with $b\geq 3.$ As another application of these techniques, we improve the known result that very general hypersurfaces in $\mathbb{P}^n$ of degree at least $2n-2$ are algebraically hyperbolic when $n\geq 6$ to $n \geq 5$, leaving $n=4$ as the only open case.
