北京雁栖湖应用数学研究院

斯拉瓦·皮缅诺夫 , 安吉尔·托莱多

Daigo Ito

2026年03月02日 16:00 至 17:00

A3-1-301

Zoom 559 700 6085 (BIMSA)

By a classical theorem of Beilinson, the perfect derived category $\operatorname{Perf}(\mathbb{P}^n)$ of projective space is equivalent to the category of derived representations of a certain quiver with relations. The vertex-wise tensor product of quiver representations corresponds to a symmetric monoidal structure $\otimes_{\mathrm{quiv}}$ on $\operatorname{Perf}(\mathbb{P}^n)$. We demonstrate that this symmetric monoidal structure can be geometrically described as an “extended convolution product.” Specifically, the Fourier--Mukai kernel is given by the closure of the torus multiplication map in $(\mathbb{P}^n)^3$. We further extend the result to any smooth proper toric variety of Bondal--Ruan type. Under toric mirror symmetry, this extended convolution product corresponds to the tensor product of constructible sheaves on a real torus.