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تسجيل مستخدم جديدTopological Abel-Jacobi map and mixed Hodge structures
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تأليف
Yilong Zhang
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For a smooth projective variety $X$ of dimension $2n-1$, Zhao defined topological Abel-Jacobi map, which sends vanishing cycles on a smooth hyperplane section $Y$ of $X$ to the middle dimensional primitive intermediate Jacobian of $X$. When the vanishing cycles are algebraic, it agrees with Griffiths Abel-Jacobi map. On the other hand, Schnell defined a topological Abel-Jacobi map using the $mathbb R$-splitting property of the mixed Hodge structure on $H^{2n-1}(Xsetminus Y)$. We show that the two definitions coincide, which answers a question of Schnell.
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