The ring of evenly weighted points on the projective line

Milena Hering, Benjamin Howard

Research output: Contribution to journalArticlepeer-review

Abstract

Let Mw = (P1)n//SL2 denote the geometric invariant theory quotient of (P1)n by
the diagonal action of SL2 using the line bundle O(w1, w2,...,wn) on (P1)n. Let Rw be the coordinate ring of Mw. We give a closed formula for the Hilbert function of Rw, which allows us to compute the degree of Mw. The graded parts of Rw are certain Kostka numbers, so this Hilbert function computes stretched Kostka numbers. If all the weights wi are even, we find a presentation of Rw so that the ideal Iw of this presentation has a quadratic Gröbner basis. In particular, Rw is Koszul. We obtain this result by studying the homogeneous coordinate ring of a projective toric variety arising as a degeneration of Mw.
Original languageEnglish
Pages (from-to)691-708
Number of pages19
JournalMathematische zeitschrift
Volume277
Issue number3-4
Early online date21 Jan 2014
DOIs
Publication statusPublished - Aug 2014

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