關於射影對偶的退化

Abstract

這篇論文的主要目標是研究射影對偶的退化。我們證明在特定條件下，一個 向量叢截面的零點集構成的光滑族的平坦極限可以描述為額外法叢截面的零點 集。作為應用，我們探討 Shinder-Zhang 的五次橢圓曲線，並證明它們會退化為 Mori-Mukai 連結中，三維二次曲面中的一條橢圓曲線。

The primary aim of this note is to initiate the study of the degenerations of projective dualities. We prove that, under certain conditions, the flat limit of a smooth family of zero loci of general sections of a vector bundle can be described as the zero locus of a section of the excess normal bundle. As an application, we examine the case of Shinder-Zhang’s degree-five elliptic curves and show that they degenerate to the elliptic curve on the quadric 3-fold, appearing in the Mori-Mukai link of Fano 3-fold.