Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal threefolds with small slope and the Noether inequality for
  canonically polarized threefolds   1) We give a 3-dimensional analogue of M. Noether's inequality for
canonically polarized threefolds: $K^3\ge 2(2p_g-5)/3$. This inequality is
sharp by known examples of M. Kobayashi.
  2) Given a minimal 3-fold $X$ of general type with canonical singularities,
if $K^3< (3p_g-5)/2$, we show that $X$ must be birationally fibred by curves of
genus 2.

5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol