Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex multiplication, Griffiths-Yukawa couplings, and rigidity for
  families of hypersurfaces   Let M(d,n) be the moduli stack of hypersurfaces of degree d > n in the
complex projective n-space, and let M(d,n;1) be the sub-stack, parameterizing
hypersurfaces obtained as a d fold cyclic covering of the projective n-1 space,
ramified over a hypersurface of degree d. Iterating this construction, one
obtains M(d,n;r).
  We show that M(d,n;1) is rigid in M(d,n), although the Griffiths-Yukawa
coupling degenerates for d<2n. On the other hand, for all d>n the sub-stack
M(d,n;2) deforms.
  We calculate the exact length of the Griffiths-Yukawa coupling over M(d,n;r),
and we construct a 4-dimensional family of quintic hypersurfaces, and a dense
set of points in the base, where the fibres have complex multiplication.

30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg