Linear systems on the blow-up of (P¹)ⁿ

2014/01/26 by Laface, Antonio, Moraga, Joaquín
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.6692

Abstract

In this note we study linear systems on the blow-up of (ℙ¹)ⁿ at r points in very general position. We prove that the fibers of the projections (ℙ¹)ⁿ → (ℙ¹)^s, 1≤ s ≤ n-1 can give contribution to the speciality of the linear system. This allows us to give a new definition of expected dimension of a linear system in (ℙ¹)ⁿ which we call fiber dimension. Finally, we state a conjecture about linear systems on (ℙ¹)³.

Related

• Standard classes on the blow-up of Pⁿ at points in very general position
• Dimension of linear systems: a combinatorial and differential approach
• Base locus of linear systems on the blowing-up of P³ along at most 8 general points
• A counterexample to a conjecture on linear systems on P³
• New methods for determining speciality of linear systems based at fat points in Pⁿ