论文标题
二元性与$ \ mathbb {q} $的关键品种相关 - fano 3倍。我
Duality Related with Key Varieties of $\mathbb{Q}$-Fano 3-folds. I
论文作者
论文摘要
抽象的。在我们以前的论文Arxiv：2210.16008中，我们表明，任何Prime $ \ Mathbb {Q} $ - Fano 3倍$ x $，只有$ 1/2（1,1,1,1）$ - 在某些5个类中的奇异性可以嵌入为线性段，以较大的dimensional $ \ mathbb {q vano-vano vano vano vano vano variities sekey sekey sekey seke key key key seke seke seke suke suke wariieties， Sarkisov Link的某些数据从爆炸中凝视着$ 1/2（1,1,1）$ - $ x $的奇异性。在本文中，我们介绍了与某种意义上双重的关键品种相关的品种。作为一个应用程序，我们将每个$ x $的sarkisov链接的基本部分解释为双重品种的线性部分。在自然背景下，描述了一个$ x $ 5的关键品种，其中一个$ 1/2（1,1,1）$ - 奇异性，我们还用$ g_ {7}^{2} $的属9属的一般规范曲线表征。
Abstract. In our previous paper arXiv:2210.16008, we show that any prime $\mathbb{Q}$-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 $\mathbb{Q}$-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 $g_{7}^{2}$.
