关于Veronese双锥的Kuznetsov分量的一个注记
A note on the Kuznetsov component of the Veronese double cone
摘要：
本文描述了Veronese双锥$Y$的导出范畴中复形的模空间。针对与理想线层具有相同类$κ_1$的对象，我们描述了Gieseker稳定层的模空间，并证明了它有两个分量。然后，我们研究了同类$Y$的Kuznetsov分支中稳定复形的模空间，它也有两个分支。一个是参数化理想线层，它出现在两个模空间中。其他组件没有直接相关的墙壁交叉：我们表明，通过描述一个中间模空间的复杂的空间的稳定对的意义上的Pandharipande和托马斯。
英文摘要：
This note describes moduli spaces of complexes in the derived category of a Veronese double cone $Y$. Focusing on objects with the same class $κ_1$ as ideal sheaves of lines, we describe the moduli space of Gieseker stable sheaves and show that it has two components. Then, we study the moduli space of stable complexes in the Kuznetsov component of $Y$ of the same class, which also has two components. One parametrizes ideal sheaves of lines and it appears in both moduli spaces. The other components are not directly related by a wall-crossing: we show this by describing an intermediate moduli space of complexes as a space of stable pairs in the sense of Pandharipande and Thomas.
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