Weighted Syzygies Library

Betti tables of weighted projective embeddings

\(H(P) = \langle 3, 5, 7 \rangle\)

Betti tables for a pointed genus 3 curve.

d =1 w =(1, 3, 5, 7) ord =(0, 3, 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	1	empty
10	empty	empty	empty
11	empty	1	empty
12	empty	empty	empty
13	empty	1	empty
14	empty	empty	empty
15	empty	empty	1
16	empty	empty	empty
17	empty	empty	1
18	empty	empty	empty

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

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

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

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

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

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