Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cone theorem and Mori hyperbolicity   We discuss the cone theorem for quasi-log schemes and the Mori hyperbolicity.
In particular, we establish that the log canonical divisor of a Mori hyperbolic
projective normal pair is nef if it is nef when restricted to the non-lc locus.
This answers Svaldi's question completely. We also treat the uniruledness of
the degenerate locus of an extremal contraction morphism for quasi-log schemes.
Furthermore, we prove that every fiber of a relative quasi-log Fano scheme is
rationally chain connected modulo the non-qlc locus.

26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
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
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat