2008/08/05 by Burt Totaro · 2 citations
Mathematics · #Abelian group #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Bundle #Commutative Algebra and Its Applications #Cone (formal languages) #Conjecture #Dimension (graph theory) #Finite field #Finitely-generated abelian group #Generalization #math.AC #math.AG #msc:13A50 #msc:14E30 #msc:14J32
paper · pdf · doi:10.1112/s0010437x08003667
26 pages. To appear in Compositio Mathematica
arxiv created 2008/08/05 · openalex publication_date 2008/09/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract We give the first examples over finite fields of rings of invariants that are not finitely generated. (The examples work over arbitrary fields, for example the rational numbers.) The group involved can be as small as three copies of the additive group. The failure of finite generation comes from certain elliptic fibrations or abelian surface fibrations having positive Mordell–Weil rank. Our work suggests a generalization of the Morrison–Kawamata cone conjecture on Calabi–Yau fiber spaces to klt Calabi–Yau pairs. We prove the conjecture in dimension two under the assumption that the anticanonical bundle is semi-ample.