论文标题
全态符号符号品种的非纤维性
Non-hyperbolicity of holomorphic symplectic varieties
论文作者
论文摘要
我们证明了原始符号性品种的非纤维性，其$ b_2 \ geq 5 $满足了理性SYZ的猜想。如果另外，如果$ b_2 \ geq 7 $，我们确定Kobayashi伪测量学的消失相同。这特别适用于当前所有已知的不可还原符号流形的例子，从而完成了Kamenova-lu-verbitsky的结果。关键的新贡献是一种带有拉格朗日纤维化的投射原始符号变化，它消失了Kobayashi伪学。该证明使用奇迹性，生育收缩和周期空间。
We prove non-hyperbolicity of primitive symplectic varieties with $b_2 \geq 5$ that satisfy the rational SYZ conjecture. If in addition $b_2 \geq 7$, we establish that the Kobayashi pseudometric vanishes identically. This in particular applies to all currently known examples of irreducible symplectic manifolds and thereby completes the results by Kamenova--Lu--Verbitsky. The key new contribution is that a projective primitive symplectic variety with a Lagrangian fibration has vanishing Kobayashi pseudometric. The proof uses ergodicity, birational contractions, and cycle spaces.
