Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On boundedness of singularities and minimal log discrepancies of
  Koll\'ar components   Recent study in K-stability suggests that klt singularities whose local
volumes are bounded away from zero should be bounded up to special
degeneration. We show that this is true in dimension three, or when the minimal
log discrepancies of Koll\'ar components are bounded from above. We conjecture
that the minimal log discrepancies of Koll\'ar components are always bounded
from above, and verify it in dimension three when the local volumes are bounded
away from zero. We also answer a question of Han, Liu and Qi on the relation
between log canonical thresholds and local volumes.

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph