Symmetric products of dg categories and semi-orthogonal decompositions

Naoki Koseki

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arXiv · 2205.09854

Symmetric products of dg categories and semi-orthogonal decompositions

Naoki Koseki

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Abstract

In this article, we investigate semi-orthogonal decompositions of the symmetric products of dg-enhanced triangulated categories. Given a semi-orthogonal decomposition $\mathcal{D}=\langle \mathcal{A}, \mathcal{B} \rangle$, we construct semi-orthogonal decompositions of the symmetric products of $\mathcal{D}$ in terms of that of $\mathcal{A}$ and $\mathcal{B}$. This was originally stated by Galkin--Shinder, and answers the question raised by Ganter--Kapranov. Combining the above result with the derived McKay correspondence, we obtain various interesting semi-orthogonal decompositions of the derived categories of the Hilbert schemes of points on surfaces.

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Naoki Koseki. 2022-05-19. Symmetric products of dg categories and semi-orthogonal decompositions. https://arxiv.org/abs/2205.09854

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