The F-signature Function on the Ample Cone
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929735655751680 |
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| author | Lee, Seungsu Pande, Suchitra |
| author_facet | Lee, Seungsu Pande, Suchitra |
| contents | For any fixed globally F-regular projective variety X over an algebraically closed field of positive characteristic, we study the F-signature of section rings of X with respect to the ample Cartier divisors on X. In particular, we define an F-signature function on the ample cone of X and show that it is locally Lipschitz continuous. We further prove that the F-signature function extends to the boundary of the ample cone. We also establish an effective comparison between the F-signature function and the volume function on the ample cone. As a consequence, we show that for divisors that are nef but not big, the extension of the F-signature is zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_00566 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The F-signature Function on the Ample Cone Lee, Seungsu Pande, Suchitra Algebraic Geometry Commutative Algebra 14B05, 14J17, 13A35, 14G17, 14C20, 14C22 For any fixed globally F-regular projective variety X over an algebraically closed field of positive characteristic, we study the F-signature of section rings of X with respect to the ample Cartier divisors on X. In particular, we define an F-signature function on the ample cone of X and show that it is locally Lipschitz continuous. We further prove that the F-signature function extends to the boundary of the ample cone. We also establish an effective comparison between the F-signature function and the volume function on the ample cone. As a consequence, we show that for divisors that are nef but not big, the extension of the F-signature is zero. |
| title | The F-signature Function on the Ample Cone |
| topic | Algebraic Geometry Commutative Algebra 14B05, 14J17, 13A35, 14G17, 14C20, 14C22 |
| url | https://arxiv.org/abs/2210.00566 |