Projective toric varieties of codimension 2 with maximal Castelnuovo--Mumford regularity

2021/06/23 by Preston Cranford, Cranford, Preston, Alan Peng +3
Computer Science · Mathematics · #05E40 (Secondary) #13D02 (Primary) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2106.12667

openalex publication_date 2021/06/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

The Eisenbud--Goto conjecture states that reg X\ledeg X -codim X+1 for a nondegenerate irreducible projective variety X over an algebraically closed field. While this conjecture is known to be false in general, it has been proven in several special cases, including when X is a projective toric variety of codimension 2. We classify the projective toric varieties of codimension 2 having maximal regularity, that is, for which equality holds in the Eisenbud--Goto bound. We also give combinatorial characterizations of the arithmetically Cohen--Macaulay toric varieties of maximal regularity in characteristic 0.

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