Weighted Syzygies Library

Betti tables of weighted projective embeddings

\(H(P) = \langle 4, 5, 7 \rangle\)

Betti tables for a pointed genus 4 curve.

d =1 w =(1, 4, 5, 7) ord =(0, 4, 5, 7)
	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	1	empty
12	empty	empty	empty
13	empty	1	empty
14	empty	1	empty
15	empty	empty	empty
16	empty	empty	empty
17	empty	empty	1
18	empty	empty	empty
19	empty	empty	empty
20	empty	empty	1
21	empty	empty	empty

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

d =3 w =(1, 2, 2, 3, 3, 3, 4, 4, 5) ord =(0, 4, 5, 7, 8, 9, 11, 12, 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	empty	empty	empty	empty	empty	empty	empty
2	empty	empty	empty	empty	empty	empty	empty	empty
3	empty	2	empty	empty	empty	empty	empty	empty
4	empty	4	1	empty	empty	empty	empty	empty
5	empty	8	6	empty	empty	empty	empty	empty
6	empty	6	15	2	empty	empty	empty	empty
7	empty	5	23	8	empty	empty	empty	empty
8	empty	2	26	23	1	empty	empty	empty
9	empty	1	21	37	6	empty	empty	empty
10	empty	empty	12	47	18	empty	empty	empty
11	empty	empty	6	41	35	2	empty	empty
12	empty	empty	2	30	47	7	empty	empty
13	empty	empty	empty	15	48	18	empty	empty
14	empty	empty	empty	6	38	28	1	empty
15	empty	empty	empty	1	21	34	4	empty
16	empty	empty	empty	empty	8	27	9	empty
17	empty	empty	empty	empty	2	17	13	empty
18	empty	empty	empty	empty	empty	6	12	1
19	empty	empty	empty	empty	empty	1	7	2
20	empty	empty	empty	empty	empty	empty	2	3
21	empty	empty	empty	empty	empty	empty	empty	1
22	empty	empty	empty	empty	empty	empty	empty	empty

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

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

d =7 w =(1, 1, 1, 1, 2) ord =(0, 4, 5, 7, 13)
	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, 4, 5, 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, 4, 5, 7, 8, 9)
	0	1	2	3	4
total	1	7	14	12	4
0	1	empty	empty	empty	empty
1	empty	6	5	empty	empty
2	empty	1	9	12	4
3	empty	empty	empty	empty	empty