Nef and Effective cones of some Quot Schemes

2024/05/07 by Chandranandan Gangopadhyay, Gangopadhyay, Chandranandan, Ronnie Sebastian +1
Mathematics · #14J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2405.04067

openalex publication_date 2024/05/07 · openalex created_date 2024/05/11 · openalex updated_date 2026/07/28

Abstract

Let C be a smooth projective curve over ℂ of genus g(C)\geqslant 3 (respectively, g(C)=2). Fix integers r,k such that 2\leqslant k\leqslant r-2, (respectively, 3\leqslant k\leqslant r-2). Let Q:=\rm Quot_C/ℂ(O^{⊕ r}_C, k, d) be the Quot scheme parametrizing rank k and degree d quotients of the trivial bundle of rank r. Let Q_L denote the closed subscheme of the Quot scheme parametrizing quotients such that the quotient sheaf has determinant L. It is known that Q_L is an integral, normal, local complete intersection, locally factorial scheme of Picard rank 2, when d≫0. In this article we compute the nef cone, effective cone and canonical divisor of this variety when d≫0. We show this variety is Fano iff r=2k+1.

Related

• Nef cones of some Quot schemes on a smooth projective curve
• Irreducibility of some nested Quot schemes
• The effective cone of the space of parametrized rational curves in a Grassmannian
• Picard Groups of Some Quot Schemes
• On the motive of zero-dimensional Quot schemes on a curve