Weighted Syzygies Library

Betti tables of weighted projective embeddings

\(H(P) = \langle 5, 6, 7, 8, 9 \rangle\)

Betti tables for a pointed genus 4 curve.

d =1 w =(1, 5, 6, 7, 8, 9) ord =(0, 5, 6, 7, 8, 9)
	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	empty	empty	empty	empty
3	empty	empty	empty	empty	empty
4	empty	empty	empty	empty	empty
5	empty	empty	empty	empty	empty
6	empty	empty	empty	empty	empty
7	empty	empty	empty	empty	empty
8	empty	empty	empty	empty	empty
9	empty	empty	empty	empty	empty
10	empty	empty	empty	empty	empty
11	empty	1	empty	empty	empty
12	empty	1	empty	empty	empty
13	empty	2	empty	empty	empty
14	empty	2	empty	empty	empty
15	empty	2	empty	empty	empty
16	empty	1	empty	empty	empty
17	empty	1	1	empty	empty
18	empty	empty	2	empty	empty
19	empty	empty	3	empty	empty
20	empty	empty	4	empty	empty
21	empty	empty	4	empty	empty
22	empty	empty	3	empty	empty
23	empty	empty	2	empty	empty
24	empty	empty	1	1	empty
25	empty	empty	empty	2	empty
26	empty	empty	empty	3	empty
27	empty	empty	empty	3	empty
28	empty	empty	empty	3	empty
29	empty	empty	empty	2	empty
30	empty	empty	empty	1	empty
31	empty	empty	empty	empty	empty
32	empty	empty	empty	empty	1
33	empty	empty	empty	empty	1
34	empty	empty	empty	empty	1
35	empty	empty	empty	empty	1
36	empty	empty	empty	empty	empty

d =2 w =(1, 3, 3, 4, 4, 5, 5) ord =(0, 5, 6, 7, 8, 9, 10)
	0	1	2	3	4	5
total	1	15	40	45	24	5
0	1	empty	empty	empty	empty	empty
1	empty	empty	empty	empty	empty	empty
2	empty	empty	empty	empty	empty	empty
3	empty	empty	empty	empty	empty	empty
4	empty	empty	empty	empty	empty	empty
5	empty	1	empty	empty	empty	empty
6	empty	2	empty	empty	empty	empty
7	empty	5	empty	empty	empty	empty
8	empty	4	2	empty	empty	empty
9	empty	3	6	empty	empty	empty
10	empty	empty	10	empty	empty	empty
11	empty	empty	12	1	empty	empty
12	empty	empty	8	6	empty	empty
13	empty	empty	2	11	empty	empty
14	empty	empty	empty	14	empty	empty
15	empty	empty	empty	9	2	empty
16	empty	empty	empty	4	6	empty
17	empty	empty	empty	empty	8	empty
18	empty	empty	empty	empty	6	empty
19	empty	empty	empty	empty	2	1
20	empty	empty	empty	empty	empty	2
21	empty	empty	empty	empty	empty	2
22	empty	empty	empty	empty	empty	empty

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

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

d =5 w =(1, 1, 2, 2, 2, 2) ord =(0, 5, 6, 7, 8, 9)
	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	empty	empty	empty	empty
3	empty	10	empty	empty	empty
4	empty	empty	20	empty	empty
5	empty	empty	empty	15	empty
6	empty	empty	empty	empty	4
7	empty	empty	empty	empty	empty

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

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

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

d =9 w =(1, 1, 1, 1, 1, 1) ord =(0, 5, 6, 7, 8, 9)
	0	1	2	3	4
total	1	6	13	12	4
0	1	empty	empty	empty	empty
1	empty	6	4	empty	empty
2	empty	empty	9	12	4
3	empty	empty	empty	empty	empty