Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Families of conic K\"ahler-Einstein metrics   Let $p:X\to Y$ be an holomorphic surjective map between compact K\"ahler
manifolds and let $D$ be an effective divisor on $X$ with generically simple
normal crossings support and coefficients in $(0,1)$. Provided that the adjoint
canonical bundle $K_{X_y}+D_y$ of the generic fiber is ample, we show that the
current obtained by glueing the fiberwise conic K\"ahler-Einstein metrics on
the regular locus of the fibration is positive. Moreover, we prove that this
current is bounded outside the divisor and that it extends to a positive
current on $X$.

21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio