Weighted Syzygies Library

Betti tables of weighted projective embeddings

\(H(P) = \langle 4, 5, 6 \rangle\)

Betti tables for a pointed genus 4 curve.

d =1 w =(1, 4, 5, 6) ord =(0, 4, 5, 6)
	0	1	2
total	1	2	1
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	empty	empty
14	empty	empty	empty
15	empty	empty	empty
16	empty	empty	empty
17	empty	empty	empty
18	empty	empty	empty
19	empty	empty	empty
20	empty	empty	1
21	empty	empty	empty

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

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

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

d =9 w =(1, 1, 1, 1, 1, 1) ord =(0, 4, 5, 6, 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