Weighted Syzygies Library

Betti tables of weighted projective embeddings

\(H(P) = \langle 3, 4 \rangle\)

Betti tables for a pointed genus 3 curve.

d =1 w =(1, 3, 4) ord =(0, 3, 4)
	0	1
total	1	1
0	1	empty
1	empty	empty
2	empty	empty
3	empty	empty
4	empty	empty
5	empty	empty
6	empty	empty
7	empty	empty
8	empty	empty
9	empty	empty
10	empty	empty
11	empty	1
12	empty	empty

d =2 w =(1, 2, 2, 3) ord =(0, 3, 4, 6)
	0	1	2
total	1	2	1
0	1	empty	empty
1	empty	empty	empty
2	empty	empty	empty
3	empty	1	empty
4	empty	empty	empty
5	empty	1	empty
6	empty	empty	empty
7	empty	empty	empty
8	empty	empty	1
9	empty	empty	empty

d =3 w =(1, 1, 2, 3) ord =(0, 3, 4, 8)
	0	1	2
total	1	3	2
0	1	empty	empty
1	empty	empty	empty
2	empty	empty	empty
3	empty	1	empty
4	empty	1	empty
5	empty	1	1
6	empty	empty	1
7	empty	empty	empty

d =4 w =(1, 1, 1) ord =(0, 3, 4)
	0	1
total	1	1
0	1	empty
1	empty	empty
2	empty	empty
3	empty	1
4	empty	empty

d =5 w =(1, 1, 1, 2, 2, 3) ord =(0, 3, 4, 9, 10, 15)
	0	1	2	3	4
total	1	10	20	15	4
0	1	empty	empty	empty	empty
1	empty	empty	empty	empty	empty
2	empty	4	1	empty	empty
3	empty	4	7	1	empty
4	empty	1	7	4	empty
5	empty	1	4	7	1
6	empty	empty	1	3	3
7	empty	empty	empty	empty	empty

d =6 w =(1, 1, 1, 1, 2) ord =(0, 3, 4, 6, 11)
	0	1	2	3
total	1	6	8	3
0	1	empty	empty	empty
1	empty	1	empty	empty
2	empty	4	4	empty
3	empty	1	4	3
4	empty	empty	empty	empty

d =7 w =(1, 1, 1, 1, 1) ord =(0, 3, 4, 6, 7)
	0	1	2	3
total	1	6	8	3
0	1	empty	empty	empty
1	empty	3	2	empty
2	empty	3	6	3
3	empty	empty	empty	empty