Generation in singularity categories of hypersurfaces of countable representation type

Tokuji Araya, Kei-ichiro Iima, Maiko Ono and Ryo Takahashi

The Orlov spectrum and Rouquier dimension are invariants of a triangulated category to measure how big the category is, and they have been studied actively. In this paper, we investigate the singularity category $D_{sg}(R)$ of a hypersurface $R$ of countable representation type. For a thick subcategory $¥mathcal{T}$ of $D_{sg}(R)$ and a full subcategory $¥mathcal{X}$ of $¥mathcal{T}$, we calculate the Rouquier dimension of $¥mathcal{T}$ with respect to $¥mathcal{X}$. Furthermore, we prove that the level in $D_{sg}(R)$ of the residue field of $R$ with respect to each nonzero object is at most one.

Archiv der Mathematik (Basel)

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