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Fano orbifolds admit free Campana curves
Brian Lehmann, Sho Tanimoto
We prove that any Fano orbifold admits a free Campana curve in the sense of Campana. Moreover, assuming that any klt log Fano pair admits a very free rational curve in its smooth l…
Finding large families of rational curves through Bend-and-Break
Eric Jovinelly, Brian Lehmann, Eric Riedl
We present a new construction that allows us to break off large-degree rational curves from families of higher genus curves. Our construction and results deepen the connection betw…
Manin's conjecture for semi-integral curves and -connectedness
Qile Chen, Brian Lehmann, Sho Tanimoto
We explore log Manin's conjecture for integral points and its connections to -connectedness. We prove log Manin's conjecture for Campana rational curves and for $\math…
A characterization of projective space via lengths of extremal rays
Osamu Fujino, Eric Jovinelly, Brian Lehmann +1
We prove a new characterization of complex projective space using lengths of extremal rays.
Geometric Manin's conjecture in characteristic
Brian Lehmann, Sho Tanimoto
Geometric Manin's conjecture for complex Fano varieties describes the structure of the moduli space of curves. We propose a version of this conjecture in characteristic and des…