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arXiv · 2601.16103

The Eisenbud-Goto conjecture for projectively normal varieties with mild singularities

Jong In Han
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Abstract

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.

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Jong In Han. 2026-01-22. The Eisenbud-Goto conjecture for projectively normal varieties with mild singularities. https://arxiv.org/abs/2601.16103

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