layout	page
title	Weierstrass Syzygies

This is a Jekyll site for organizing Betti tables of section rings associated to pointed curves and their Weierstrass semigroups. It accompanies the paper Weighted Syzygies of Pointed Curves by Maya Banks, John Cobb, and Mahrud Sayrafi.

The display layer uses the reusable [betti-table.html]({{ site.baseurl }}/) include. Table data is stored under _data/weierstrass/, with one YAML file for each computed semigroup. Each record contains:

• the section-ring parameter $d$;
• the generator weights and pole orders;
• total Betti numbers by homological degree;
• nonzero entries, with x marking support outside the bound and . marking a possible support position.

The source format follows yamlBettiTables in Pinkham.m2: it computes section rings for $d=1,\ldots,2g+1$, extracts minimalBetti, and records the sorted pairs of weighted degree and pole order. The TeX files remain the reference for the visual translation.

Pages for genera 2 through 5 display computed Betti tables. The bound-only pages for genera 5 through 10 are generated by _plugins/betti_bounds.rb; their Betti entries are intentionally left uncomputed. On semigroup-specific pages, j and l move to the preceding and following semigroups of the same genus.

The supplied genus-count sequence for $0\leq g\leq 10$ is $$1, 1, 2, 4, 7, 12, 23, 39, 67, 118, 204.$$

Kunz-cone visualizations will use the same data directory and can be added as a separate include without coupling them to table rendering.