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# Mathematical Research Letters

## Volume 25 (2018)

### Number 4

### Section rings of $\mathbb{Q}$-divisors on minimal rational surfaces

Pages: 1329 – 1357

DOI: http://dx.doi.org/10.4310/MRL.2018.v25.n4.a13

#### Authors

#### Abstract

We bound the degrees of generators and relations of section rings associated to arbitrary $\mathbb{Q}$-divisors on projective spaces of all dimensions and Hirzebruch surfaces. For section rings of effective $\mathbb{Q}$-divisors on projective spaces, we find the best possible bound on the degrees of generators and relations.

Supported by the National Science Foundation (grant number DMS-1250467).

Received 27 August 2015