Unirationality of varieties described by families of projective hypersurfaces

2022/05/26 by Ciro Ciliberto, Ciliberto, Ciro, Duccio Sacchi +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2205.13260

openalex publication_date 2022/05/26 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

Abstract

Let \mathscrX→ W be a flat family of generically irreducible hypersurfaces of degree d≥ 2 in \PPⁿ with singular locus of dimension t, with W unirational of dimension r. We prove that if n is large enough with respect to d, r and t, then \mathscrX is unirational. This extends results in \cite Pre, HMP.

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