2009/03/31 by Abdelmoubine Amar Henni
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number #Algebraic structures and combinatorial models #Algebraic variety #Functor #Geometry #Mathematical analysis #Mathematics #Moduli space #Monad (category theory) #Noetherian #Projective plane #Projective variety #Pure mathematics #Torsion (gastropod) #math.AG #msc:14D20 #msc:14D21 #msc:14J60
paper · pdf · doi:10.1142/s0129167x14500086
published as International Journal of Mathematics Vol. 25, No. 01, 1450008 (2014) · 32 pages
arxiv created 2011/08/23 · openalex publication_date 2014/01/01 · arxiv updated 2019/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct monads for framed torsion-free sheaves on blow-ups of the complex projective plane at finitely many distinct points. Using these monads we prove that the moduli space of such sheaves is a smooth algebraic variety. Moreover, we construct monads for families of such sheaves parametrized by a noetherian scheme S of finite type. A universal monad on the moduli space is introduced and used to prove that the moduli space is fine.