Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lowest Weights in Cohomology of Variations of Hodge Structure (II)   Let $X$ be an irreducible complex analytic space with $j:U\into X$ an
immersion of a smooth Zariski open subset, and let $\bV$ be a variation of
Hodge structure of weight $n$ over $U$. Assume $X$ is compact K\"ahler. Then
provided the local monodromy operators at infinity are quasi-unipotent,
$IH^k(X, \bV)$ is known to carry a pure Hodge structure of weight $k+n$, while
$H^k(U,\bV)$ carries a mixed Hodge structure of weight $\ge k+n$. In this note
it is shown that the image of the natural map $IH^k(X,\bV) \to H^k(U,\bV)$ is
the lowest weight part of this mixed Hodge structure. In the algebraic case
this easily follows from the formalism of mixed sheaves, but the analytic case
is rather complicated, in particular when the complement $X-U$ is not a
hypersurface.

19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex