Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative Proportionality for subvarieties of moduli spaces of K3 and
  abelian surfaces   The relative proportionality principle of Hirzebruch and H\"ofer was
discovered in the case of compactified ball quotient surfaces X when studying
curves C in X. It can be expressed as an inequality which attains equality
precisely when C is an induced quotient of a subball. A similar inequality
holds for curves on Hilbert modular surfaces. In this paper we prove a
generalization of this result to subvarieties of Shimura varieties of
orthogonal type, i.e. locally symmetric spaces for the Lie group SO(n,2).
Furthermore we study the ''inverse problem'' of deciding when an arbitrary
subvariety Z of M is of Hodge type, provided it contains sufficiently many
divisors W_i which are of Hodge type and satisfy relative proportionality.

36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th