论文标题
Fano三倍的切线束的束缚与Picard第二
Bigness of the tangent bundle of a Fano threefold with Picard number two
论文作者
论文摘要
在本文中，我们研究了带有Picard Number 2的Fano三倍$ x $的切线捆绑$ t_x $的积极属性。我们确定了整个36个变形类型的切线束的bigness。我们的结果表明，只有$（-K_X）^3 \ ge 34 $，$ t_x $很大。作为推论，我们证明当$ x $具有标准的圆锥捆结构和非空的判别物时，切线束并不大。我们的主要方法是在$ \ mathbb {p}（t_x）$上产生不可约的有效除数，该$是从与理性曲线家族相关的总双VMRT构建的。此外，我们提出了一些标准，以确定$ t_x $的bigness。
In this paper, we study the positivity property of the tangent bundle $T_X$ of a Fano threefold $X$ with Picard number 2. We determine the bigness of the tangent bundle of the whole 36 deformation types. Our result shows that $T_X$ is big if and only if $(-K_X)^3\ge 34$. As a corollary, we prove that the tangent bundle is not big when $X$ has a standard conic bundle structure with non-empty discriminant. Our main methods are to produce irreducible effective divisors on $\mathbb{P}(T_X)$ constructed from the total dual VMRT associated to a family of rational curves. Additionally, we present some criteria to determine the bigness of $T_X$.
