For a P^1-orbifold C, we prove that its big quantum cohomology is generically
semisimple. As a corollary, we verify a conjecture of Dubrovin for orbi-curves. We also
show that the small quantum cohomology of C is generically semisimple iff C is Fano, i.e.
it has positive orbifold Euler characteristic.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/3207