Exceptional Collections in Sn-equivariant Derived Categories

Student: Mironov Mikhail

Supervisor: Aleksandr Kuznetsov

Educational Programme: Mathematics and Mathematical Physics (Master)

Year of Graduation: 2017

Обозначим через $X_{n,k}$ произведение $k$ копий $n$-мерного проективного пространства: $\mathbb {P}^n \times \mathbb {P}^n \times \dots \times \mathbb {P}^n$. На $X_{n,k}$ действует группа перестановок $G = S_k$, переставляющая $\mathbb {P}^n$. Обозначим через $\coh^G (X_{n,k})$ категорию $G$-equivariant coherent sheaves on $X_{n,k}$. From the category $\coh^G (X_{n,k})$ we can construct bounded derived category $\cD^b(\coh^G (X_{n,k}))$. Our main goal is to construct rectangular Lefschetz decomposition of $\cD^b(\coh^G (X_{n,k}))$.

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