Lefschetz Properties of complete intersesctions and maximal variation of hyperplane sections
Year: 2026
Type: preprint
Abstract: For an artinian complete intersection of forms of degree $d$, we prove that the multiplication by a general linear form is injective up to degree $\frac{3d-1}2$, independently of the number of variables. This is accomplished using algebraic and geometric properties of the union of two complete intersection curves and their general hyperplane sections. As a consequence, we solve, for any $d\ge 4$, the problem about the maximal variation of the hyperplane sections of a smooth hypersurface of degree $d$ posed by A. Beauville.
Source: arXiv (Cornell University)
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Vetenskapsrådet
OpenAlex ID: W7223058364