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

Aaron Landesman (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)

Peter Ruhm (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)

Robin Zhang (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

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.

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

Received 27 August 2015