Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inequality of Noether Type for Gorenstein Minimal 3-folds of General
  Type   Let $X$ be a Gorenstein minimal $3$-fold of general type. We prove the
optimal inequality: $$K_X^{3}\geq \frac{4}{3}\chi(\omega_X)-2,$$ where
$\chi(\omega_X)$ is the Euler-Poincar$\acute{\text{e}}$ characteristic of the
dualizing sheaf $\o_{X}$.

34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
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
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs