29 citations · 127 across the 38 of their papers we have counts for
42 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…
On Manin's conjecture for quartic del Pezzo fibrations
Sho Tanimoto
We generalize the homological sieve method, developed by Das, Lehmann, Tosteson, and the author, to study certain quartic del Pezzo fibrations, and we prove a version of Manin's co…
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…
Homological sieve and Manin's conjecture
Sho Tanimoto
This is a report of the author's talk at RIMS workshop Algebraic Number Theory and Related Topics 2025 which was held at RIMS Kyoto University during December 15th-19th 2025. In th…
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…
Intermediate Jacobians and Burnside invariants
Andrew Kresch, Sho Tanimoto, Yuri Tschinkel
We propose new invariants in equivariant birational geometry, combining equivariant intermediate Jacobians and the Burnside formalism, for smooth rationally connected threefolds wi…
Homological stability and weak approximation
Sho Tanimoto, Yuri Tschinkel
We investigate homological stability for the space of sections of Fano fibrations over curves in the context of weak approximation, and establish it for projective bundles, as well…
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…
The spaces of rational curves on del Pezzo surfaces via conic bundles
Sho Tanimoto
Using the homological sieve method developed by Das--Lehmann--Tosteson and the author, we prove Peyre's all height approach to Manin's conjecture for split quintic del Pezzo surfac…
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…
Campana points on wonderful compactifications
Dylon Chow, Daniel Loughran, Ramin Takloo-Bighash +1
We prove a variant of Manin's conjecture for Campana points on wonderful compactifications of semi-simple algebraic groups of adjoint type. We use this to provide evidence for a ne…
Intermediate Jacobians and linearizability
Tudor Ciurca, Sho Tanimoto, Yuri Tschinkel
We develop an equivariant version of the formalism of intermediate Jacobian torsor obstructions, and apply it to conic bundles over rational surfaces, quadric surface bundles over…
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…
Non-free curves on Fano varieties
Brian Lehmann, Eric Riedl, Sho Tanimoto
Let be a smooth Fano variety over and let be a smooth projective curve over . Geometric Manin's Conjecture predicts the structure of the irreducibl…
Non-free sections of Fano fibrations
Brian Lehmann, Eric Riedl, Sho Tanimoto
Let be a smooth projective curve and let be a smooth integral model of a geometrically integral Fano variety over . Geometric Manin's Conjecture pr…
An introduction to Geometric Manin's conjecture
Sho Tanimoto
This is a survey paper on Geometric Manin's conjecture which was proposed by Brian Lehmann and the author. We introduce Geometric Manin's conjecture (GMC) and review some recent pr…
Rational curves on del Pezzo surfaces in positive characteristic
Roya Beheshti, Brian Lehmann, Eric Riedl +1
We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most primes p we prove the irreducibility of the moduli space of rational curves of a gi…
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…
Campana points, Height zeta functions, and log Manin's conjecture
Sho Tanimoto
This is a report of the author's talk at RIMS workshop 2020 Problems and Prospects in Analytic Number Theory held online on Zoom. We discuss a recent formulation of log Manin's con…
The spaces of rational curves on del Pezzo threefolds of degree one
Nobuki Shimizu, Sho Tanimoto
We prove the irreducibility of moduli spaces of rational curves on a general del Pezzo threefold of Picard rank and degree . As corollaries, we confirm Geometric Manin's con…
Moduli spaces of rational curves on Fano threefolds
Roya Beheshti, Brian Lehmann, Eric Riedl +1
We prove several classification results for the components of the moduli space of rational curves on a smooth Fano threefold. In particular, we prove a conjecture of Batyrev on the…
Movable Bend and Break for sections of del Pezzo fibrations
Sho Tanimoto
This is a report of the author's talk at Algebra Symposium 2019 held at Tohoku University. We discuss some improvements of Mori's Bend and Break for sections of del Pezzo fibration…
Classifying sections of del Pezzo fibrations, I
Brian Lehmann, Sho Tanimoto
We develop a strategy to classify the components of the space of sections of a del Pezzo fibration over . In particular, we prove the Movable Bend and Break lemma f…