The space of rational curves and Manin's conjecture

Sho Tanimoto (Copenhagen)

Manin's conjecture is a conjectural asymptotic formula for the counting function of rational points on a Fano variety after removing an exceptional set and with Brian Lehmann, we have been studying birational geometry of exceptional sets in Manin's conjecture using the minimal model program and the boundedness of Fano varieties. Recently we found some applications of our study to questions regarding the space of rational curves, its dimension and the number of irreducible components. In this talk I would like to explain these developments. This is joint work with Brian Lehmann.

Tuesday, April 25th, at 4:00pm in HBH 227

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