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· DOI 10.1007/s13348-026-00509-y

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math.AG 1

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2026 1

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On the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$

math.AG · 2026-04-27 · unverdicted · novelty 6.0

Explicit formulas express the dimension and degree of the singular subscheme of hypersurfaces in P^n via the graded Betti numbers of the Jacobian algebra, producing new restrictions on those Betti numbers and a dimension result for homologically strictly plus-one generated hypersurfaces.

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  • On the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$ math.AG · 2026-04-27 · unverdicted · none · ref 4

    Explicit formulas express the dimension and degree of the singular subscheme of hypersurfaces in P^n via the graded Betti numbers of the Jacobian algebra, producing new restrictions on those Betti numbers and a dimension result for homologically strictly plus-one generated hypersurfaces.