Optimal algebraic tangent cone of torsion-free sheaves via valuations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917239437918208 |
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| author | Hada, Yohei |
| author_facet | Hada, Yohei |
| contents | We develop a valuation-theoretic framework for studying tangent cones of torsion-free sheaves on algebraic varieties. To analyze these objects, we introduce a slope stability theory, including the Harder-Narasimhan filtrations, for finitely generated $\mathbb{R}$-graded modules over finitely generated $\mathbb{R}_{\geq 0}$-graded algebras. Using it, we show that there is a canonically determined tangent cone of torsion-free sheaves, up to the expected equivalence ambiguity, for quasi-regular valuations, which generalize Chen-Sun [3]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01112 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal algebraic tangent cone of torsion-free sheaves via valuations Hada, Yohei Algebraic Geometry Differential Geometry We develop a valuation-theoretic framework for studying tangent cones of torsion-free sheaves on algebraic varieties. To analyze these objects, we introduce a slope stability theory, including the Harder-Narasimhan filtrations, for finitely generated $\mathbb{R}$-graded modules over finitely generated $\mathbb{R}_{\geq 0}$-graded algebras. Using it, we show that there is a canonically determined tangent cone of torsion-free sheaves, up to the expected equivalence ambiguity, for quasi-regular valuations, which generalize Chen-Sun [3]. |
| title | Optimal algebraic tangent cone of torsion-free sheaves via valuations |
| topic | Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2602.01112 |