In-Person Talk 

Suppose we fix a smooth Fano variety X and a smooth projective curve C.  Certain components of Mor(C,X) will be "pathological" (e.g. will have larger than expected dimension).  By analogy with Manin's Conjecture over number fields, Geometric Manin's Conjecture predicts that the "pathological" components of Mor(C,X) are controlled by the Fujita invariant.  I will discuss some recent results elucidating this relationship. 

This is joint work with Eric Riedl and with Sho Tanimoto.