Interpolating Lagrangian Skeleta and variation of GIT

par Zhou Peng

vendredi 17 mai 2019, 10:30 → 11:30 Europe/Paris

112 (ICJ)

Let $\mathbb{C}^*$ act on $\mathbb{C}^n$ with weights $(a_1, ..., a_n)$, such that the $a_i$'s are non-zero are not of the same sign. Then there are two non-empty stacky quotients $[\mathbb{C}^n / \mathbb{C}^*]$, denoted as $X(-)$ and $X(+)$. It is well-known that the spaces $X(+)$ and $X(-)$ are related by an elementary flip. The flip has a mirror description using Fukaya-Seidel category, developed by Kerr. Here, we give an alternative description of the flip, given by a window skeleton $L$ in the cotangent bundle of a cylinder $T^*( T^{n-1}\times R)$, that connects the skeleton $L(+)$ and $L(-)$ which are mirror to the quotient $X(-)$ and $X(+)$. This is inspired by the window-category approach to variation of GIT problem, following idea of Kontsevich and Diemer.