5 citations · 8 across the 3 of their papers we have counts for
7 papers · 1 filter
Classifying sections of del Pezzo fibrations, II
Brian Lehmann, Sho Tanimoto
Let be a del Pezzo surface over the function field of a complex curve. We study the behavior of rational points on leading to bounds on the counting function in Geometric M…
Restricted tangent bundles for general free rational curves
Brian Lehmann, Eric Riedl
Suppose that is a smooth projective variety and that is a general member of a family of free rational curves on . We prove several statements showing that the Harder-Nar…
Rational curves on prime Fano threefolds of index 1
Brian Lehmann, Sho Tanimoto
We study the moduli spaces of rational curves on prime Fano threefolds of index 1. For general threefolds of most genera we compute the dimension and the number of irreducible comp…
On exceptional sets in Manin's Conjecture
Brian Lehmann, Sho Tanimoto
In this survey paper we study Manin's Conjecture from a geometric perspective. The focus of the paper is the recent conjectural description of the exceptional set in Manin's Conjec…
Iitaka dimension for cycles
Brian Lehmann
We define the Iitaka dimension of a numerical cycle class and develop its theory. We conjecture that the Iitaka dimension is integer-valued, and give some evidence in this directio…
Positivity of the diagonal
Brian Lehmann, John Christian Ottem
We study how the geometry of a projective variety is reflected in the positivity properties of the diagonal considered as a cycle on . We analyze when the dia…