Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Burniat surfaces II: secondary Burniat surfaces form three connected
  components of the moduli space   We prove in one go that each of the 4 families of Burniat surfaces with K^2 =
6,5,4, is a connected component of the moduli space of surfaces of general
type.
  We prove also the rationality of each component. In the nodal case (one of
the two families for K^2_S = 4) a very surprising and new phenomenon occurs.
  Both the moduli space for the minimal models and the Gieseker moduli space
for canonical models are everywhere non reduced.
  But the nilpotence order is higher for the first.

30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin