Title: Section rings of Q-divisors on stacky curves and minimal rational surfaces
Speaker: Robin Zhang (Columbia University)
Time: 2018-1-10, 16:00-17:00
Place: N817
Abstract: Consider modular forms arising from a fi nite-area quotient of the upper-half plane by a Fuchsian group. By the classical results of Kodaira-Spencer, this ring of modular forms may be viewed as the log spin canonical ring of a stacky curve. We find tight bounds on the degrees of minimal generators and relations of these section rings. We also consider section rings associated to arbitrary Q-divisors on projective spaces of all dimensions and Hirzebruch surfaces with an eye towards potential applications to rings of Hilbert modular forms and Siegel modular forms. We find bounds on the degrees of their generators and relations. For section rings of effective Q-divisors on projective spaces, we fi nd the best possible bound on the degrees of generators and relations.