Venue: MCM110
Title: Instructive graded ring calculation for orbifold curves, K3 surfaces and Fano 3-folds
Abstract: A question that turns out to be extremely entertaining and instructive concern the graded ring over an orbifold curve C of genus 2 marked with distinct points P + Q in |KC|, and polarized by the fractional divisor 1/2*P + 3/5*Q. Theorem 1 says that C is the weighted plane curve C(11) in PP(1,2,5). The calculation provides an opportunity to explain many points around orbifold RR, that are elementary but deserve to be better known.
Theorem 1 forms base camp for an ascent to one interesting case of a K3 surface and a Fano 3-fold of codimension 5.
GRDB list more than 50,000 candidate Hilbert series of Fano 3-folds, of which only around 1,000 have been seriously studied and partly understood. Current joint work with SUZUKI Kaori successfully constructs a case of #41058, and corrects the GRDB entry for #41245
