Cox rings of blow-ups of multiprojective spaces

2023/08/22 by Bolognesi, Michele, Massarenti, Alex, Poma, Elena
#14N05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 14E30 #Rings and Algebras (math.RA) #Secondary 14M99

paper · doi:10.48550/arxiv.2308.11283

Abstract

Let X^1,n_r be the blow-up of ℙ¹×ℙⁿ in r general points. We describe the Mori cone of X^1,n_r for r≤ n+2 and for r = n+3 when n≤ 4. Furthermore, we prove that X^1,n_n+1 is log Fano and give an explicit presentation for its Cox ring.

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