Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitesimal variation functions for families of smooth varieties   In this paper we introduce some {\it variation functions} associated to the
rank of the Infinitesimal Variations of Hodge Structure for a family of smooth
projective complex curves. We give some bounds and inequalities and, in
particular, we prove that if $X$ is a smooth plane curve $X$, then there exists
a first order deformation $\xi\in H^1(T_X)$ which deforms $X$ as plane curve,
such that $\xi\cdot:H^0(\omega_X)\to H^1(\mathcal{O}_{X})$ is an isomorphism.
We also generalize the notions of variation functions to the higher dimensional
case and we analyze the link between IVHS and the Weak and Strong Lefschetz
properties of the Jacobian ring of a smooth hypersurface.

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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex