4 papers
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…
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.
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…
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…