Rationality Proofs by Curve Counting

Figures & data

Table 1. Curve counts for $(a,b,c)=(2,4,4),$ n = 3, k = 2.

$\det (H)$	8	16	24	32	36	40	44	48	56	64
$\#C$	0	0,1	4	8,10,18	8	20	24	48,60	80	212

Table 2. Curve counts for $(a,b,c)=(2,3,6),$ n = 4, k = 1.

$\det (H)$	144	432	576	864	1296
$\#C$	1	6	12	0	72