2022/11/13 by Hiromichi Takagi, Takagi, Hiromichi
Mathematics · Arts and Humanities · #Algebraic Geometry and Number Theory #Caribbean and African Literature and Culture #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2211.06784
Abstract. In our previous paper arXiv:2210.16008, we show that any prime ℚ-Fano 3-folds X with only 1/2(1,1,1)-singularities in certain 5 classes can be embedded as linear sections into bigger dimensional ℚ-Fano varieties called key varieties, where each of the key varieties is constructed from certain data of the Sarkisov link staring from the blow-up at one 1/2(1,1,1)-singularity of X. In this paper, we introduce varieties associated with the key varieties which are dual in a certain sense. As an application, we interpret a fundamental part of the Sarkisov link for each X as a linear section of the dual variety. In a natural context describing the variety dual to the key variety of X of genus 5 with one 1/2(1,1,1)-singularity, we also characterize a general canonical curve of genus 9 with a g72.