2015/09/16 by Uwe Nagel, Nagel, Uwe, Alexandra Seceleanu +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #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.1509.04977
openalex publication_date 2015/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fermat ideals define planar point configurations that are closely related to\nthe intersection locus of the members of a specific pencil of curves. These\nideals have gained recent popularity as counterexamples to some proposed\ncontainments between symbolic and ordinary powers. We give a systematic\ntreatment of the family of Fermat ideals, describing explicitly the minimal\ngenerators and the minimal free resolutions of all their ordinary powers as\nwell as many symbolic powers. We use these to study the ordinary and the\nsymbolic Rees algebra of Fermat ideals. Specifically, we show that the symbolic\nRees algebras of Fermat ideals are Noetherian. Along the way, we give formulas\nfor the Castelnuovo-Mumford regularity of the powers of Fermat ideals and we\ndetermine their reduction ideals.\n