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math.AG2025
Free curves and fundamental groups
Eric Jovinelly, Brian Lehmann, Eric Riedl
We show that klt Fano varieties and certain lc Fano varieties contain free higher-genus curves in their smooth loci. Our methods also allow us to find free curves on varieties in p…
math.AG2025
Optimal bounds in Bend-and-Break
Eric Jovinelly, Brian Lehmann, Eric Riedl
We improve the Bend-and-Break result of Miyaoka and Mori by establishing the optimal degree bound. Our result also yields optimal bounds on lengths of extremal rays of log canonica…
math.AG2025
Homological stability and Manin's conjecture for rational curves on quartic del Pezzo surfaces
Ronno Das, Brian Lehmann, Sho Tanimoto +1
We prove a version of Manin's conjecture (over for large) and the Cohen--Jones--Segal conjecture (over ) for maps from rational curves to split qua…