Positivity of divisors on blown-up projective spaces, II

Abstract

We construct log resolutions of pairs on the blow-up of the projective space in an arbitrary number of general points and we discuss the semi-ampleness of the strict transforms. As an application we prove that the abundance conjecture holds for an infinite family of such pairs. For $n+2$ points, these strict transforms are F-nef divisors on the moduli space ${\overline{\mathcal{M}}}_{0,n+3}$ in a Kapranov's model: we show that all of them are nef.

Journal of Algebra

References in corpus (4)

• On blowing up the weighted projective plane
• On the Fano variety of linear spaces contained in two odd-dimensional quadrics
• Birational geometry of the moduli space of rank 2 parabolic vector bundles on a rational curve
• A note on the very ampleness of complete linear systems on blowings-up of P^3

Cited by in corpus (4)

• Cones of effective divisors on the blown-up P^3 in general lines
• Seshadri constants on some blow-ups of projective spaces
• Bilinear secants and birational geometry of blowups of ${\mathbb{P}}^n\times {\mathbb{P}}^{n+1}$
• The blow-up of ${\mathbb{P}}^4$ at 8 points and its Fano model, via vector bundles on a del Pezzo surface