Bertini Theorems for F-signature and Hilbert-Kunz multiplicity

2017/10/31 by Javier Carvajal-Rojas, Javier Carvajal‐Rojas, Karl Schwede +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Combinatorics #Geometry #Geometry and complex manifolds #Hilbert space #Hyperplane #Lambda #Mathematical analysis #Mathematics #Multiplicity (mathematics) #Physics #Pure mathematics #Signature (topology) #math.AC #math.AG #msc:13A35 #msc:14B05 #msc:14F18 #msc:14J17

paper · pdf · doi:10.1007/s00209-021-02712-y

published as Math. Z. 299 (2021), no. 1-2, 1131--1153 · 23 pages, typos corrected and proofs improved, to appear in Math. Z

arxiv created 2021/02/12 · openalex publication_date 2021/03/05 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that Bertini theorems hold for F-signature and Hilbert--Kunz multiplicity. In particular, if X ⊆ ℙⁿ is normal and quasi-projective with F-signature greater than λ (respectively the Hilbert--Kunz multiplicity is less than λ) at all points x ∈ X, then for a general hyperplane H ⊆ ℙⁿ the F-signature (respectively Hilbert--Kunz multiplicity) of X ∩ H is greater than λ (respectively less than λ) at all points x ∈ X ∩ H.

Citations

• Birational Geometry of Algebraic Varieties
• Bertini and his two fundamental theorems
• Characterizations of Regular Local Rings of Characteristic p
• Two theorems about maximal Cohen-Macaulay modules
• F-signature and Hilbert–Kunz multiplicity : a combined approach and comparison
• Algebraic Geometry