Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On blowing up extremal K\"ahler manifolds   We show that the blowup of an extremal Kahler manifold at a relatively stable
point in the sense of GIT admits an extremal metric in Kahler classes that make
the exceptional divisor sufficiently small, extending a result of
Arezzo-Pacard-Singer. We also study the K-polystability of these blowups,
sharpening a result of Stoppa in this case. As an application we show that the
blowup of a Kahler-Einstein manifold at a point admits a constant scalar
curvature Kahler metric in classes that make the exceptional divisor small, if
it is K-polystable with respect to these classes.

21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ