Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential geometric global smoothings of simple normal crossing
  complex surfaces with trivial canonical bundle   Let $X$ be a simple normal crossing compact complex surface with trivial
canonical bundle which includes at most triple intersections. We prove that if
$X$ is $d$-semistable, then there exists a family of smoothings in a
differential geometric sense. This extends the smoothability result of R.
Friedman to cases where not all irreducible components of $X$ are K\"{a}hlerian
or $H^1(X, \mathcal{O}_X)$ does not vanish. The proof is based on an explicit
construction of local smoothings around the singular locus of $X$, and the
first author's existence result of holomorphic volume forms on global
smoothings of $X$. In particular, these volume forms are given as solutions of
a nonlinear elliptic partial differential equation.
  As an application, we provide several examples of $d$-semistable simple
normal crossing complex surfaces with trivial bundle including double curves,
which are smoothable to complex tori, primary Kodaira surfaces and $K3$
surfaces. We also provide several examples of such complex surfaces including
triple points, which are smoothable to $K3$ surfaces.

18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas