具有光滑射影曲线上同调的光滑仿射曲面
On smooth affine surfaces with the cohomology of a smooth projective curve
AI总结：
本文针对具有正亏格光滑射影曲线有理混合霍奇结构的光滑复仿射曲面，证明其存在到该曲线的光滑态射，纤维为仿射直线，是Jouanolou技巧在二维的逆命题。
AI中文摘要：
我们证明，若光滑复仿射曲面具有正亏格光滑射影曲线的有理混合霍奇结构，则它允许到该曲线的光滑态射，其纤维同构于仿射直线。特别地，每个此类曲面都是该曲线上线丛的挠子的全空间。该结果的动机源于Jouanolou技巧，此结果为二维情形下Jouanolou技巧提供了一种逆命题。
英文摘要：
We prove that if a smooth affine complex surface has the same rational mixed Hodge structure as a smooth projective curve of positive genus, then it admits a smooth morphism to the curve with fibers isomorphic to affine line. In particular, every such surface is the total space of a torsor for a line bundle on the curve. The motivation comes from Jouanolou's trick, to which this result gives a kind of converse in dimension 2.
