Fedder type criteria for quasi-$F$-splitting I
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912722274222080 |
|---|---|
| author | Kawakami, Tatsuro Takamatsu, Teppei Yoshikawa, Shou |
| author_facet | Kawakami, Tatsuro Takamatsu, Teppei Yoshikawa, Shou |
| contents | Yobuko recently introduced the notion of quasi-$F$-splitting and quasi-$F$-split heights, which generalize and quantify the notion of Frobenius-splitting, and proved that quasi-$F$-split heights coincide with Artin-Mazur heights for Calabi-Yau varieties. In this paper, we prove Fedder type criteria for quasi-$F$-splittings of complete intersections, and in particular, obtain a simple formula to compute Artin-Mazur heights of Calabi-Yau hypersurfaces. As one of its applications, we prove that there exist Calabi-Yau varieties of arbitrarily high Artin-Mazur height over $\mathbb{F}_2$. We also give explicit defining equations of quartic K3 surfaces over $\mathbb{F}_{3}$ realizing all the possible Artin-Mazur heights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_10076 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fedder type criteria for quasi-$F$-splitting I Kawakami, Tatsuro Takamatsu, Teppei Yoshikawa, Shou Algebraic Geometry Commutative Algebra Number Theory 13A35, 13F35, 14J32, 14B05 Yobuko recently introduced the notion of quasi-$F$-splitting and quasi-$F$-split heights, which generalize and quantify the notion of Frobenius-splitting, and proved that quasi-$F$-split heights coincide with Artin-Mazur heights for Calabi-Yau varieties. In this paper, we prove Fedder type criteria for quasi-$F$-splittings of complete intersections, and in particular, obtain a simple formula to compute Artin-Mazur heights of Calabi-Yau hypersurfaces. As one of its applications, we prove that there exist Calabi-Yau varieties of arbitrarily high Artin-Mazur height over $\mathbb{F}_2$. We also give explicit defining equations of quartic K3 surfaces over $\mathbb{F}_{3}$ realizing all the possible Artin-Mazur heights. |
| title | Fedder type criteria for quasi-$F$-splitting I |
| topic | Algebraic Geometry Commutative Algebra Number Theory 13A35, 13F35, 14J32, 14B05 |
| url | https://arxiv.org/abs/2204.10076 |