Higher Nash Blowups of A₃-Singularity

2018/04/30 by Rin Toh-Yama, Toh-Yama, Rin
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1804.11050

openalex publication_date 2018/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the n -th Nash blowup of the toric surface singularity of type A₃ is singular for any n > 0 . It was known that the normalization of the n -th Nash blowup of a toric variety is also a toric variety associated to the Gröbner fan of a certain ideal J_n . In our case, we prove that the Gröbner fan contains a non-regular cone. We determine minimal generators of the initial ideal of J_n with respect to a certain monomial ordering, and show that the reduced Gröbner basis of J_n has polynomials of certain forms for each n .

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