Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Newton nondegenerate Weil divisors in toric varieties   We introduce and develop the theory of Newton nondegenerate local Weil
divisors $(X,0)$ in toric affine varieties. We characterize in terms of the
toric combinatorics of the Newton diagram different properties of such singular
germs: normality, Gorenstein property, or being an Cartier divisor in the
ambient space. We discuss certain properties of their (canonical) resolution
$\tilde{X}\to X $ and the corresponding canonical divisor. We provide
combinatorial formulae for the delta--invariant $\delta(X,0)$ and for the
cohomology groups $H^i(\tilde X,\mathcal{O}_{\tilde X})$ for $i>0$. In the case
$\dim(X,0)=2$, we provide the (canonical) resolution graph from the Newton
diagram and we also prove that if such a Weil divisor is normal and Gorenstein,
and the link is a rational homology sphere, then the geometric genus is given
by the minimal path cohomology, a topological invariant of the link.

22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con