These papers are organized in reverse chronological order.
| Approximating rational points on surfaces (joint with D. McKinnon, M. Satriano) submitted |
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| On the asymptotic enumerativity property for Fano manifolds (joint with R. Beheshti, C. Lian, E. Riedl, J. Starr, S. Tanimoto) submitted |
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| Non-free curves on Fano varieties (joint with E. Riedl, S. Tanimoto) to appear on Osaka J. Math. |
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| Non-free sections of Fano fibrations (joint with E. Riedl, S. Tanimoto) submitted |
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| Rational curves on del Pezzo surfaces in positive characteristic (joint with R. Beheshti, E. Riedl, S. Tanimoto) Trans. Amer. Math. Soc. 10 (2023), 407451 |
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| Classifying sections of del Pezzo fibrations, II (joint with S. Tanimoto) Geom. & Top. 26 (2022), no. 6, 2565-2647 |
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| Restricted tangent bundles for general free rational curves (joint with E. Riedl) Int. Math. Res. Not. (2023), no. 12, 9901-9949 |
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| Moduli spaces of rational curves on Fano threefolds (joint with R. Beheshti, E. Riedl, S. Tanimoto) Adv. Math. 408 (2022), Paper No. 108557 |
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| Classifying sections of del Pezzo fibrations, I (joint with S. Tanimoto) J. Eur. Math. Soc. 26 (2024), no. 1, 289–354 |
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| Rational curves on prime Fano threefolds of index 1 (joint with S. Tanimoto) J. Alg. Geom. 30 (2021), no. 1, 151-188 Errata (joint with E. Jovinelly, S. Tanimoto): pdf |
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| On exceptional sets in Manin’s Conjecture (joint with S. Tanimoto) Res. Math. Sci. 6 (2019), no. 1, Paper No. 12, 41 pp. |
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| Geometric consistency of Manin’s Conjecture (joint with A.K. Sengupta, S. Tanimoto) Compos. Math. 158 (2022), no. 6, 1375-1427 |
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| Iitaka dimension for cycles Trans. Amer. Math. Soc. 371 (2019), no. 7, 4815-4835 |
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| Positivity of the diagonal (joint with J.C. Ottem) Adv. Math. 335 (2018), 664-695 |
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| Geometric Manin’s Conjecture and rational curves (joint with S. Tanimoto) Compos. Math. 155 (2019), no. 5, 833-862 Errata: The formulation of Geometric Manin’s Conjecture is not quite correct. The definition of the \alpha-constant in the paper is incorrect; the (well-known) typical definition should be used instead. Also, Conjecture 6.5 is incorrect; it should be modified by looking at algebraic instead of numerical equivalence. |
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| Correspondences between convex geometry and complex geometry (joint with J. Xiao) EpiGA 1 (2017), Art. 6 |
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| On the geometry of thin exceptional sets in Manin’s Conjecture (joint with S. Tanimoto) Duke Math. J. 166 (2017), no. 15, 2815-2869 Errata: the proof of Proposition 7.2 is not complete. In the erratum we prove a slightly weaker statement which suffices for all applications in the paper. The statement of Proposition 7.2 is also true by an argument of Chen Jiang (personal communication). |
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| Positivity functions for curves on algebraic varieties (joint with J. Xiao) Algebra Number Theory 13 (2019), no. 6, 1243-1279 |
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| Convexity and Zariski decomposition structure (joint with J. Xiao) Geom. Funct. Anal. 26 (2016), no. 4, 1135-1189 |
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| Volume and Hilbert function of R-divisors (joint with M. Fulger and J. Kollár) Mich. Math. J. 65 (2016), no. 2, 371-387 |
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| Balanced line bundles on Fano varieties (joint with S. Tanimoto and Y. Tschinkel) J. Reine Angew. Math. 743 (2018), 91-131 |
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| Positive cones of dual cycle classes (joint with M. Fulger) Alg. Geom. 4 (2017), no. 1, 1-28 |
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| Morphisms and faces of pseudo-effective cones (joint with M. Fulger) Proc. Lon. Math. Soc. 112 (2016), no. 4, 651-676 |
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| Kernels of numerical pushforwards (joint with M. Fulger) Adv. Geom. 17 (2017), no. 3, 373-378 |
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| Zariski decompositions of numerical cycle classes (joint with M. Fulger) J. Alg. Geom. 26 (2017), no. 1, 43-106 Errata: Angela Gibney has informed me there are some mistakes in the calculations for symmetrized M_0,7. See this paper by Han-Bom Moon for some correct calculations. |
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| Asymptotic behavior of the dimension of the Chow variety Adv. Math. 308 (2017), 815-835 Errata: When publishing the paper I was completely unaware that the calculation of the dimension of the Chow variety of P^n was done previously by Pablo Azcue in his 1992 thesis “On the dimension of Chow varieties” under Joe Harris at Harvard. I would like to sincerely apologize for the inadvertent failure to credit Azcue for this result. |
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| Volume-type functions for numerical cycle classes Duke Math. J. 165 (2016), no. 16, 3147-3187 |
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| The movable cone via intersections | ||
| Numerical triviality and pullbacks J. Pure Appl. Algebra 219 (2015), no. 12, 5637-5649 |
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| Algebraic bounds on analytic multiplier ideals Ann. Inst. Fourier 64 (2014), no. 3, 1077-1108 Errata: In the statement of Theorem 1.4 this paper inherits the ambiguity about the definition of abundance from “On Eckl’s pseudo-effective reduction map”. See the errata of that paper for a discussion of which definition must be used. |
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| On Eckl’s pseudo-effective reduction map Trans. Amer. Math. Soc. 366 (2014), 1525-1549 Errata: Due to the errors in “Comparing numerical dimensions”, one must be careful about which numerical dimension is used in this paper. See here for a careful discussion. |
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| Comparing numerical dimensions Algebra Number Theory 7 (2013), no. 5, 1065-1100 Errata: As demonstrated by this paper by John Lesieutre, the statement of the main theorem is incorrect. There is a mistake in the proof of Proposition 5.3 which invalidates one step in the long chain of inequalities used to prove the main theorem. This error was first pointed out to me by Thomas Eckl. To the best of my knowledge all other parts of the paper are correct: the paper establishes new inequalities between various definitions of the numerical dimension. The corrected statements can be found here or in Lesieutre’s paper. |
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| Reduction maps and minimal model theory (joint with Y. Gongyo) Compos. Math. 149 (2013), no. 2, 295-308 Errata: In the proof of Theorem 4.3, we use a result of Noboru Nakayama. Osamu Fujino has informed me that the proof in the citation is incomplete, but it is fixed in this note by Fujino. Due to the error in “Comparing numerical dimensions”, one must be careful about which version of the numerical dimension is used. In this paper we are using kappa_sigma as defined by Nakayama. As explained in the errata to “On Eckl’s pseudo-effective reduction map”, the main results of that paper are compatible with this definition. |
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| A cone theorem for nef curves J. of Alg. Geom. 21 (2012), no. 3, 473-493 |
Expository papers: here are a couple survey papers related to different areas of my research.
| A snapshot of the Minimal Model Program Proc. of Symp. in Pure Math. 95 (2017), AMS, 1-32 |
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| An introduction to volume functions for algebraic cycles | ||
| On exceptional sets in Manin’s Conjecture (joint with S. Tanimoto) Res. Math. Sci. 6 (2019), no. 1, Paper No. 12, 41 pp. |
Long versions: here are longer versions of a couple papers. Warning: there may be errors in these papers that are not in the published versions.