Weighted Syzygies Library

Betti tables of weighted projective embeddings

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

Betti tables for a pointed genus 4 curve.

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

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

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

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

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

d =7 w =(1, 1, 1, 1, 2, 2, 3) ord =(0, 3, 5, 6, 13, 14, 21)
	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	7	8	1	empty	empty
3	empty	5	15	11	1	empty
4	empty	1	11	15	5	empty
5	empty	1	5	14	11	1
6	empty	empty	1	4	7	4
7	empty	empty	empty	empty	empty	empty

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

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