2015/12/08 by Mohsen Asgharzadeh, Asgharzadeh, Mohsen · 1 citation
Mathematics · #13A35 #13D40 #14H60 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1512.02518
openalex publication_date 2015/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the (LC) conjecture of Hochster and Huneke in some non-trivial cases. This has several applications. Recently, Brenner and Caminata answered a numerical evidence due to Dao and Smirnov on the shape of generalized Hilbert-Kunz functions of smooth curves. As applications, we first reprove this by a short argument. Then we give a proof of second numerical evidence predicted by Dao and Smirnov on the shape of generalized Hilbert-Kunz functions of nodal curves. Thirdly, we answer a question posted by Vraciu on the (LC) property of a proposed ring. Inspiring with the (LC) property, we present a connection to the stability theory. This leads us to investigate the stability and the strong semistability of the sheaf of relations on \x2,y2,z2\ over the Klein's quartic curve. This answers questions of Brenner. After presenting a connection from (LC) to the F-threshold, we answer a question posted by Huneke et al. Additional applications and examples are given.