Weighted Syzygies Library

Betti tables of weighted projective embeddings

\(H(P) = \langle 4, 6, 7, 9 \rangle\)

Betti tables for a pointed genus 4 curve.

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

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

d =4 w =(1, 1, 2, 2, 3) ord =(0, 4, 6, 7, 9)
	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) ord =(0, 4, 6, 7, 9, 10, 15)
	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	1	empty	empty	empty	empty
3	empty	10	3	empty	empty	empty
4	empty	3	21	3	empty	empty
5	empty	1	13	18	1	empty
6	empty	empty	3	21	7	empty
7	empty	empty	empty	3	15	1
8	empty	empty	empty	empty	1	4
9	empty	empty	empty	empty	empty	empty

d =6 w =(1, 1, 1, 2, 2, 2) ord =(0, 4, 6, 7, 9, 11)
	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, 4, 6, 7, 9)
	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, 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, 4, 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