Duality related with key varieties of ℚ-Fano threefolds constructed from projective bundles
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Hiromichi Takagi
Abstract
In our previous paper [31], we show that all primeℚ-Fano 3-folds X with only 1/2(1, 1, 1)-singularities in certain 5 classes can be embedded as linear sections into bigger dimensionalℚ-Fano varieties called key varieties; each key variety is constructed from data of the Sarkisov link starting 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
Funding statement: This work is supported in part by Grant-in Aid for Scientific Research (C) 16K05090.
Acknowledgements
I am grateful to Professor Shinobu Hosono for his encouragement while writing this paper. Through previous collaborations with him, my understanding about linear duality was deepened and this led me to Theorem 2.3. A strong motivation to obtain results in this paper came from Professor Mukai’s other side of works [23; 24]. From personal conversations with him, I learned a lot of things about this. I appreciate him giving me a lot of ideas generously. I am grateful to the referee for making valuable comments and suggestions which improved the presentation of this paper.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Duality related with key varieties of ℚ-Fano threefolds constructed from projective bundles
- Continuous CM-regularity and generic vanishing
- Quotient spaces of K3 surfaces by non-symplectic involutions fixing a curve of genus 8 or more
- A note on polarized varieties with high nef value
- Anisotropic area-preserving nonlocal flow for closed convex plane curves
- New sextics of genus 6 and 10 attaining the Serre bound
- The balanced superelliptic mapping class groups are generated by three elements
- Bach flow of simply connected nilmanifolds
Articles in the same Issue
- Frontmatter
- Duality related with key varieties of ℚ-Fano threefolds constructed from projective bundles
- Continuous CM-regularity and generic vanishing
- Quotient spaces of K3 surfaces by non-symplectic involutions fixing a curve of genus 8 or more
- A note on polarized varieties with high nef value
- Anisotropic area-preserving nonlocal flow for closed convex plane curves
- New sextics of genus 6 and 10 attaining the Serre bound
- The balanced superelliptic mapping class groups are generated by three elements
- Bach flow of simply connected nilmanifolds
