论文标题
DG类别和半正交分解的对称产品
Symmetric products of dg categories and semi-orthogonal decompositions
论文作者
论文摘要
在本文中，我们研究了DG增强三角剖分类别的对称产物的半正交分解。给定半正交分解$ \ MATHCAL {d} = \ langle \ Mathcal {a}，\ Mathcal {b} \ rangle $，我们以$ \ \ \ \ \ \ $ \ n co {b的$ \ n and of $ \ mathcal {d} $的对称产品的半正交分解构建这最初是由Galkin-Shinder所说的，并回答了Ganter-Kapranov提出的问题。将上述结果与派生的McKay对应关系相结合，我们获得了表面上Hilbert Hilbert方案的派生类别的各种有趣的半正交分解。
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.
