论文标题
在某些哈塞特空间上的出色收藏
Exceptional collections on certain Hassett spaces
论文作者
论文摘要
我们构建了一个$ s_2 \ times s_n $在Hassett稳定稳定曲线的空间上，有$ n+2 $标记和权重$（\ frac {1} {2} {2} {2} {2}+η，\ frac {1} {1} {1} {2} {2}+η，ε，ε，\ ldots $ and $ and $ and $ and $ and $和0 <用$（\ mathbb {p}^1）^n $的对称git标识通过$ \ mathbb {g} _m $的对角动作，当$ n $是奇数时，当$ n $时，当$ n $均为$ n $时。这样的特殊集合的存在是所需的成分之一，以证明在$ \ overline {\ mathcal {m}} _ {0，n} $上存在完整的$ s_n $ invariant extubiant collectiant collectiant collectial集合。为了证明异常，我们在派生类别中使用Windows的方法。为了证明充实，我们使用以前的工作，这些工作是在Losev-Manin空间上存在不变的特殊收藏。
We construct an $S_2\times S_n$ invariant full exceptional collection on Hassett spaces of weighted stable rational curves with $n+2$ markings and weights $(\frac{1}{2}+η, \frac{1}{2}+η,ε,\ldots,ε)$, for $0<ε, η\ll1$ and can be identified with symmetric GIT quotients of $(\mathbb{P}^1)^n$ by the diagonal action of $\mathbb{G}_m$ when $n$ is odd, and their Kirwan desingularization when $n$ is even. The existence of such an exceptional collection is one of the needed ingredients in order to prove the existence of a full $S_n$-invariant exceptional collection on $\overline{\mathcal{M}}_{0,n}$. To prove exceptionality we use the method of windows in derived categories. To prove fullness we use previous work on the existence of invariant full exceptional collections on Losev-Manin spaces.
