Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Abel-Jacobi map and mixed Hodge structures   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 $H^{2n-1}(X\setminus Y)$. We show that the two definitions
coincide, which answers a question of Schnell.

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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th