Log Fano blowups of mixed products of projective spaces and their effective cones

2021/09/08 by Grange, Tim, Postinghel, Elisa, Prendergast-Smith, Artie
#14C20 #14J45 #14J70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.03736

Abstract

We compute the cones of effective divisors on blowups of ℙ¹ × ℙ² and ℙ¹ × ℙ³ in up to 6 points. We also show that all these varieties are log Fano, giving a conceptual explanation for the fact that all the cones we compute are rational polyhedral.

Related

• Cones of effective divisors on the blown-up P³ in general lines
• Some examples of log Fano structures on blow-ups along subvarieties in products of two projective spaces
• Log Fano structures and Cox rings of blow-ups of products of projective spaces
• Cox rings of blow-ups of multiprojective spaces
• Cones of effective cycles on blow ups of projective spaces along rational curves