1 citations · 1 across the 9 of their papers we have counts for
12 papers
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…
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…
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…
Codimension of jumping loci
Brian Lehmann, Eric Riedl, Sho Tanimoto
Suppose that is a vector bundle on a smooth projective variety . Given a family of curves on , we study how the Harder-Narasimhan filtration of $\mathcal{E}…
Campana rational connectedness and weak approximation
Qile Chen, Brian Lehmann, Sho Tanimoto
Campana introduced a notion of Campana rational connectedness for Campana orbifolds. Given a Campana fibration over a complex curve, we prove that a version of weak approximation f…
Approximating rational points on surfaces
Brian Lehmann, David McKinnon, Matthew Satriano
Let be a smooth projective algebraic variety over a number field and in . In 2007, the second author conjectured that, in a precise sense, if rational points on $…
On the asymptotic enumerativity property for Fano manifolds
Roya Beheshti, Brian Lehmann, Carl Lian +3
We study the enumerativity of Gromov-Witten invariants where the domain curve is fixed in moduli and required to pass through the maximum possible number of points. We say a Fano m…