Morphisms to noncommutative projective lines
| Autor: | Daniel Chan, Adam Nyman |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
Degree (graph theory) Applied Mathematics General Mathematics Invertible sheaf Field (mathematics) Mathematics - Rings and Algebras Noncommutative geometry Combinatorics Mathematics - Algebraic Geometry Elliptic curve Cover (topology) Rings and Algebras (math.RA) Projective line Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Abelian category Algebraic Geometry (math.AG) |
| DOI: | 10.48550/arxiv.1912.02921 |
| Popis: | 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. Minor corrections made. Final version, to appear in Proc. Amer. Math. Soc |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|