New relations on Caporaso-Harris invariants and more


Yu-Jong Tzeng

15:30:00 - 17:00:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Caporaso-Harris invariants count the number of nodal curves on the projective plane satisfying given tangency conditions with a line. Those invariants are first proved to satisfy a recursive formula in 1996 and then showed to be polynomials in the degree (when the degree is large enough) using tropical geometry in 2009. On the other hand, the number of nodal curves are already known to be universal polynomials of the Chern numbers for any surfaces and line bundles. In this talk we will discuss a new type of relations for Caporaso-Harris invariants which unify these features and in fact also hold on all smooth varieties.