On Seshadri constants of adjoint divisors on surfaces and threefolds in arbitrary characteristic
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915752361066496 |
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| author | Rösler, Linus |
| author_facet | Rösler, Linus |
| contents | We develop a new approach towards obtaining lower bounds of the Seshadri constants of ample adjoint divisors on smooth projective varieties $X$ in arbitrary characteristic. Let $x\in X$ be a closed point and $A$ an ample divisor on $X$. If $X$ is a surface, we recover some known lower bounds by proving, e.g., that $\varepsilon(K_X+4A;x)\geq 3/4$. If $X$ is a threefold, we prove that for all $δ>0$ and all but finitely many curves $C$ through $x$, we have $\frac{(K_X+6A).C}{\operatorname{mult}_x C}\geq\frac{1}{2\sqrt{2}}-δ$. In particular, if $\varepsilon(K_X+6A;x)<1/(2\sqrt{2})$, then $\varepsilon(K_X+6A;x)$ is a rational number, attained by a Seshadri curve $C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16094 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Seshadri constants of adjoint divisors on surfaces and threefolds in arbitrary characteristic Rösler, Linus Algebraic Geometry Primary 14C20, 14J30, Secondary 13H15 We develop a new approach towards obtaining lower bounds of the Seshadri constants of ample adjoint divisors on smooth projective varieties $X$ in arbitrary characteristic. Let $x\in X$ be a closed point and $A$ an ample divisor on $X$. If $X$ is a surface, we recover some known lower bounds by proving, e.g., that $\varepsilon(K_X+4A;x)\geq 3/4$. If $X$ is a threefold, we prove that for all $δ>0$ and all but finitely many curves $C$ through $x$, we have $\frac{(K_X+6A).C}{\operatorname{mult}_x C}\geq\frac{1}{2\sqrt{2}}-δ$. In particular, if $\varepsilon(K_X+6A;x)<1/(2\sqrt{2})$, then $\varepsilon(K_X+6A;x)$ is a rational number, attained by a Seshadri curve $C$. |
| title | On Seshadri constants of adjoint divisors on surfaces and threefolds in arbitrary characteristic |
| topic | Algebraic Geometry Primary 14C20, 14J30, Secondary 13H15 |
| url | https://arxiv.org/abs/2601.16094 |