Weighted Syzygies Library

Betti tables of weighted projective embeddings

\(H(P) = \langle 3, 7, 8 \rangle\)

Betti tables for a pointed genus 4 curve.

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

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

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

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

d =5 w =(1, 1, 2, 2, 2, 2, 3, 3) ord =(0, 3, 7, 8, 9, 10, 14, 15)
	0	1	2	3	4	5	6
total	1	21	70	105	84	35	6
0	1	empty	empty	empty	empty	empty	empty
1	empty	empty	empty	empty	empty	empty	empty
2	empty	2	empty	empty	empty	empty	empty
3	empty	10	6	empty	empty	empty	empty
4	empty	6	24	6	empty	empty	empty
5	empty	3	26	27	2	empty	empty
6	empty	empty	12	44	16	empty	empty
7	empty	empty	2	22	36	4	empty
8	empty	empty	empty	6	24	14	empty
9	empty	empty	empty	empty	6	15	2
10	empty	empty	empty	empty	empty	2	4
11	empty	empty	empty	empty	empty	empty	empty

d =6 w =(1, 1, 1, 2, 2, 2, 2) ord =(0, 3, 6, 7, 8, 10, 11)
	0	1	2	3	4	5
total	1	15	40	45	24	5
0	1	empty	empty	empty	empty	empty
1	empty	1	empty	empty	empty	empty
2	empty	4	4	empty	empty	empty
3	empty	10	16	6	empty	empty
4	empty	empty	20	24	4	empty
5	empty	empty	empty	15	16	1
6	empty	empty	empty	empty	4	4
7	empty	empty	empty	empty	empty	empty

d =7 w =(1, 1, 1, 1, 2, 2) ord =(0, 3, 6, 7, 8, 11)
	0	1	2	3	4
total	1	10	20	15	4
0	1	empty	empty	empty	empty
1	empty	1	empty	empty	empty
2	empty	6	6	empty	empty
3	empty	3	12	9	empty
4	empty	empty	2	6	4
5	empty	empty	empty	empty	empty

d =8 w =(1, 1, 1, 1, 1) ord =(0, 3, 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, 3, 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