Weighted Syzygies Library

Betti tables of weighted projective embeddings

\(H(P) = \langle 2, 7 \rangle\)

Betti tables for a pointed genus 3 curve.

d =1 w =(1, 2, 7) ord =(0, 2, 7)
	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	1
14	empty	empty

d =2 w =(1, 1, 4) ord =(0, 2, 7)
	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	1
8	empty	empty

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

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

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

d =6 w =(1, 1, 1, 1, 2, 2, 2) ord =(0, 2, 4, 6, 7, 9, 11)
	0	1	2	3	4	5
total	1	15	40	45	24	5
0	1	empty	empty	empty	empty	empty
1	empty	3	2	empty	empty	empty
2	empty	6	12	6	empty	empty
3	empty	6	18	18	6	empty
4	empty	empty	8	18	12	2
5	empty	empty	empty	3	6	3
6	empty	empty	empty	empty	empty	empty

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