Explicit log Fano structures on blow-ups of projective spaces

Abstract

In this paper we determine which blow-ups $X$ of ${\mathbb{P}}^n$ at general points are log Fano, that is, when there exists an effective $\mathbb{Q}$-divisor $\Delta$ such that $-(K_X+\Delta )$ is ample and the pair $(X,\Delta )$ is klt. For these blow-ups, we produce explicit boundary divisors $\Delta$ making $X$ log Fano.

30 pages

References in corpus (2)

• On the anti-canonical ring and varieties of Fano type
• On the effective cone of ${\mathbb{P}}^n$ blown-up at $n+3$ points

Cited by in corpus (10)

• On the Fano variety of linear spaces contained in two odd-dimensional quadrics
• Positivity of divisors on blown-up projective spaces, II
• On the birational geometry of spaces of complete forms I: collineations and quadrics
• Birational geometry of moduli spaces of configurations of points on the line
• Spherical blow-ups of Grassmannians and Mori Dream Spaces
• Birational geometry of blow-ups of projective spaces along points and lines
• Bilinear secants and birational geometry of blowups of ${\mathbb{P}}^n\times {\mathbb{P}}^{n+1}$
• Some examples of log Fano structures on blow-ups along subvarieties in products of two projective spaces
• On the rigidity of moduli of weighted pointed stable curves
• The blow-up of ${\mathbb{P}}^4$ at 8 points and its Fano model, via vector bundles on a del Pezzo surface