2017/03/27 by Lutz Hille, LUTZ HILLE, David Ploog +1
Mathematics · #Abelian group #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Endomorphism #Equivalence (formal languages) #Exact sequence #Extension (predicate logic) #Rational surface #Rings, Modules, and Algebras #Sequence (biology) #math.AG #math.RT #msc:14F05 #msc:16E35 #msc:16S48 #msc:18E30
paper · pdf · doi:10.1017/nmj.2017.40
published as Nagoya Math. J. 235 (2019) 26-41 · 13 pages
arxiv created 2017/03/27 · openalex created_date 2017/04/07 · openalex publication_date 2017/12/20 · arxiv updated 2019/07/31 · openalex updated_date 2026/08/05
We introduce the notion of exact tilting objects, which are partial tilting objects T inducing an equivalence between the abelian category generated by T and the category of modules over the endomorphism algebra of T . Given a chain of sufficiently negative rational curves on a rational surface, we construct an exceptional sequence whose universal extension is an exact tilting object. For a chain of (-2) -curves, we obtain an equivalence with modules over a well-known algebra.