论文标题
Veronese双锥的Kuznetsov组件上的注释
A note on the Kuznetsov component of the Veronese double cone
论文作者
论文摘要
本说明描述了Veronese双锥$ y $的派生类别中的复合物的模量空间。我们专注于相同类$κ_1$作为理想线条的对象，我们描述了Gieseker稳定搁板的模量空间，并表明它具有两个组件。然后，我们研究了同一类的$ y $的Kuznetsov组件中稳定复合物的模量空间，该组件还具有两个组件。一个参数为理想的线条，并出现在两个模量空间中。其他组件并非通过墙壁交叉直接相关：我们通过将复合物的中间模量描述为pandharipande和Thomas的中间模量作为稳定对的空间。
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.
