Geodesic
On Knörrer Periodicity for Quadric Hypersurfaces in Skew Projective Spaces
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 896-911

Voir la notice de l'article provenant de la source Cambridge University Press

We study the structure of the stable category $\text{}\underline{\mathsf{CM}}^{\mathbb{Z}}(S/(f))$ of graded maximal Cohen–Macaulay module over $S/(f)$ where $S$ is a graded ($\pm 1$)-skew polynomial algebra in $n$ variables of degree 1, and $f=x_{1}^{2}+\cdots +x_{n}^{2}$. If $S$ is commutative, then the structure of $\text{}\underline{\mathsf{CM}}^{\mathbb{Z}}(S/(f))$ is well known by Knörrer’s periodicity theorem. In this paper, we prove that if $n\leqslant 5$, then the structure of $\text{}\underline{\mathsf{CM}}^{\mathbb{Z}}(S/(f))$ is determined by the number of irreducible components of the point scheme of $S$ which are isomorphic to $\mathbb{P}^{1}$.
DOI : 10.4153/S0008439518000607
Mots-clés : Knörrer periodicity, stable category, noncommutative quadric hypersurface, skew polynomial algebra, point scheme 
Ueyama, Kenta. On Knörrer Periodicity for Quadric Hypersurfaces in Skew Projective Spaces. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 896-911. doi: 10.4153/S0008439518000607
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