2019/11/28 by James A. Green, Green, James
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1911.12671
openalex publication_date 2019/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let E be the tilting bundle on the Grassmannian Gr(n,r) of r-dimensional quotients of \Bbbkn constructed by Kapranov. Buchweitz, Leuschke and Van den Bergh introduced a quiver Q and a surjective \Bbbk-algebra homomorphism Φ\colon\Bbbk Q→ A=End(E), together with a recipe on how the kernel may be computed. In this paper, for the case r=2 we give a new, direct proof that Φ is surjective and then complete the picture by calculating the ideal of relations explicitly. As an application, we then use this presentation to show that Gr(n,2) is isomorphic to a fine moduli space of certain stable A-modules, just as ℙn can be recovered from the endomorphism algebra of Beilinson's tilting bundle \bigoplus0≤ i≤ nOℙn(i).