Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morphisms to noncommutative projective lines   Let $k$ be a field, let ${\sf C}$ be a $k$-linear abelian category, let
$\underline{\mathcal{L}}:=\{\mathcal{L}_{i}\}_{i \in \mathbb{Z}}$ be a sequence
of objects in ${\sf C}$, and let $B_{\underline{\mathcal{L}}}$ be the
associated orbit algebra. We describe sufficient conditions on
$\underline{\mathcal{L}}$ such that there is a canonical morphism from the
noncommutative space ${\sf Proj }B_{\underline{\mathcal{L}}}$ to a
noncommutative projective line in the sense of \cite{abstractp1}, generalizing
the usual construction of a map from a scheme $X$ to $\mathbb{P}^{1}$ defined
by an invertible sheaf $\mathcal{L}$ generated by two global sections. We then
apply our results to construct, for every natural number $d>2$, a degree two
cover of Piontkovski's $d$th noncommutative projective line by a noncommutative
elliptic curve in the sense of Polishchuk.

37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics