The Eisenbud-Goto conjecture for projectively normal varieties with mild singularities
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915785611411456 |
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| author | Han, Jong In |
| author_facet | Han, Jong In |
| contents | For a nondegenerate projective variety $X$, the Eisenbud-Goto conjecture asserts that $\operatorname{reg}X\leq\operatorname{deg}X-\operatorname{codim}X+1$. Despite the existence of counterexamples, identifying the classes of varieties for which the conjecture holds remains a major open problem. In this paper, we prove that the Eisenbud-Goto conjecture holds for $2$-very ample projectively normal varieties with factorial, rational, hypersurface singularities and isolated Gorenstein singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Eisenbud-Goto conjecture for projectively normal varieties with mild singularities Han, Jong In Algebraic Geometry Primary 14N05, Secondary 13D02 For a nondegenerate projective variety $X$, the Eisenbud-Goto conjecture asserts that $\operatorname{reg}X\leq\operatorname{deg}X-\operatorname{codim}X+1$. Despite the existence of counterexamples, identifying the classes of varieties for which the conjecture holds remains a major open problem. In this paper, we prove that the Eisenbud-Goto conjecture holds for $2$-very ample projectively normal varieties with factorial, rational, hypersurface singularities and isolated Gorenstein singularities. |
| title | The Eisenbud-Goto conjecture for projectively normal varieties with mild singularities |
| topic | Algebraic Geometry Primary 14N05, Secondary 13D02 |
| url | https://arxiv.org/abs/2601.16103 |