Positivity of divisors on blown-up projective spaces, I

Abstract

We study $l$-very ample, ample and semi-ample divisors on the blown-up projective space ${\mathbb{P}}^n$ in a collection of points in general position. We establish Fujita's conjectures for all ample divisors with the number of points bounded above by $2n$ and for an infinite family of ample divisors with an arbitrary number of points.

arXiv commentInequality (2.2) was slightly modified

Cited by in corpus (2)

• Positivity of divisors on blown-up projective spaces, II
• Seshadri constants on some blow-ups of projective spaces