Weighted Syzygies Library

Betti tables of weighted projective embeddings

These tables show the support bounds from Theorem 2.2.

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

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

\(H(P) = \langle 3, 4 \rangle\)

Betti tables for a pointed genus 3 curve.

d =1 w =(1, 3, 4) ord =(0, 3, 4)
	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	1
12	empty	empty

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

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

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

d =6 w =(1, 1, 1, 1, 2) ord =(0, 3, 4, 6, 11)
	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, 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

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

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

\(H(P) = \langle 4, 5, 6, 7 \rangle\)

Betti tables for a pointed genus 3 curve.

d =1 w =(1, 4, 5, 6, 7) ord =(0, 4, 5, 6, 7)
	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	1	empty	empty
10	empty	1	empty	empty
11	empty	2	empty	empty
12	empty	1	empty	empty
13	empty	1	empty	empty
14	empty	empty	1	empty
15	empty	empty	2	empty
16	empty	empty	2	empty
17	empty	empty	2	empty
18	empty	empty	1	empty
19	empty	empty	empty	empty
20	empty	empty	empty	1
21	empty	empty	empty	1
22	empty	empty	empty	1
23	empty	empty	empty	empty

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

d =3 w =(1, 2, 2, 2, 3, 3, 3) ord =(0, 4, 5, 6, 7, 8, 9)
	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	3	empty	empty	empty	empty
4	empty	6	2	empty	empty	empty
5	empty	6	12	empty	empty	empty
6	empty	empty	18	6	empty	empty
7	empty	empty	8	18	empty	empty
8	empty	empty	empty	18	6	empty
9	empty	empty	empty	3	12	empty
10	empty	empty	empty	empty	6	2
11	empty	empty	empty	empty	empty	3
12	empty	empty	empty	empty	empty	empty

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

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