Weighted Syzygies Library

Betti tables of weighted projective embeddings

\(H(P) = \langle 2, 9 \rangle\)

Betti tables for a pointed genus 4 curve.

d =1 w =(1, 2, 9) ord =(0, 2, 9)
	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	empty
12	empty	empty
13	empty	empty
14	empty	empty
15	empty	empty
16	empty	empty
17	empty	1
18	empty	empty

d =2 w =(1, 1, 5) ord =(0, 2, 9)
	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	1
10	empty	empty

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

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

d =5 w =(1, 1, 1, 2, 2, 3) ord =(0, 2, 4, 9, 10, 15)
	0	1	2	3	4
total	1	9	17	12	3
0	1	empty	empty	empty	empty
1	empty	1	empty	empty	empty
2	empty	2	2	empty	empty
3	empty	4	4	1	empty
4	empty	1	6	3	empty
5	empty	1	4	4	1
6	empty	empty	1	4	1
7	empty	empty	empty	empty	1
8	empty	empty	empty	empty	empty

d =6 w =(1, 1, 1, 1, 2, 2) ord =(0, 2, 4, 6, 9, 11)
	0	1	2	3	4
total	1	9	16	9	1
0	1	empty	empty	empty	empty
1	empty	3	2	empty	empty
2	empty	3	6	3	empty
3	empty	3	6	3	empty
4	empty	empty	2	3	empty
5	empty	empty	empty	empty	1
6	empty	empty	empty	empty	empty

d =7 w =(1, 1, 1, 1, 2, 2, 2, 2, 3) ord =(0, 2, 4, 6, 9, 11, 13, 14, 21)
	0	1	2	3	4	5	6	7
total	1	28	112	210	224	140	48	7
0	1	empty	empty	empty	empty	empty	empty	empty
1	empty	3	2	empty	empty	empty	empty	empty
2	empty	9	18	9	empty	empty	empty	empty
3	empty	12	39	42	15	empty	empty	empty
4	empty	3	35	72	51	11	empty	empty
5	empty	1	15	57	76	36	3	empty
6	empty	empty	3	27	60	51	15	empty
7	empty	empty	empty	3	21	36	21	3
8	empty	empty	empty	empty	1	6	9	4
9	empty	empty	empty	empty	empty	empty	empty	empty

d =8 w =(1, 1, 1, 1, 1, 2, 2, 2, 2) ord =(0, 2, 4, 6, 8, 9, 11, 13, 15)
	0	1	2	3	4	5	6	7
total	1	28	112	210	224	140	48	7
0	1	empty	empty	empty	empty	empty	empty	empty
1	empty	6	8	3	empty	empty	empty	empty
2	empty	12	36	36	12	empty	empty	empty
3	empty	10	48	84	64	18	empty	empty
4	empty	empty	20	72	96	56	12	empty
5	empty	empty	empty	15	48	54	24	3
6	empty	empty	empty	empty	4	12	12	4
7	empty	empty	empty	empty	empty	empty	empty	empty

d =9 w =(1, 1, 1, 1, 1, 1) ord =(0, 2, 4, 6, 8, 9)
	0	1	2	3	4
total	1	10	20	15	4
0	1	empty	empty	empty	empty
1	empty	6	8	3	empty
2	empty	4	12	12	4
3	empty	empty	empty	empty	empty