论文标题
Segre Cutic的同源二元性二元性
Homological projective duality for the Segre cubic
论文作者
论文摘要
Segre Cutic和Castelnuovo-Richmond四分之一是在$ \ Mathbb {P}^4 $中的两个投影双重性曲面，其历史悠久，历史悠久。我们将解释Kuznetsov的同源射双二元性理论如何将这种投影二重性提升到Segre立方的小分辨率的派生类别与Coble Fourdold的小解决方案之间的关系，这是$ \ Mathbb {P}^4 $沿Castelnuoovo-Richond-Richondond-Richond-Richond-Richond-Richond-Richond-Richond-Richond-Richond Quartic Quartic Quartic Quartic Quartic Quartic Quartic Quartic Quartic Quartic的双重封面。 然后，同源射双二元性提供了线性部分的派生类别的描述，我们将描述该类别以说明理论。 Segre Cutic和Coble四倍的情况不足以表现出有趣的行为，同时很容易解释这种特殊且非常古典的情况。
The Segre cubic and Castelnuovo-Richmond quartic are two projectively dual hypersurfaces in $\mathbb{P}^4$, with a long and rich history starting in the 19th century. We will explain how Kuznetsov's theory of homological projective duality lifts this projective duality to a relationship between the derived category of a small resolution of the Segre cubic and a small resolution of the Coble fourfold, the double cover of $\mathbb{P}^4$ ramified along the Castelnuovo-Richmond quartic. Homological projective duality then provides a description of the derived categories of linear sections, which we will describe to illustrate the theory. The case of the Segre cubic and Coble fourfold is non-trivial enough to exhibit interesting behavior, whilst being easy enough to explain the general machinery in this special and very classical case.
