Weighted Syzygies Library

Betti tables of weighted projective embeddings

These tables show the support bounds from Theorem 2.2.

\(H(P) = \langle 2, 5 \rangle\)

Betti tables for a pointed genus 2 curve.

d =1 w =(1, 2, 5) ord =(0, 2, 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	1
10	empty	empty

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

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

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

\(H(P) = \langle 3, 4, 5 \rangle\)

Betti tables for a pointed genus 2 curve.

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

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

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

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

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