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Award ID contains: 1945144

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  1. ; (, International Mathematics Research Notices)
    Abstract Suppose that $$X$$ is a smooth projective variety and that $$C$$ is a general member of a family of free rational curves on $$X$$. We prove several statements showing that the Harder–Narasimhan filtration of $$T_{X}|_{C}$$ is approximately the same as the restriction of the Harder–Narasimhan filtration of $$T_{X}$$ with respect to the class of $$C$$. When $$X$$ is a Fano variety, we prove that the set of all restricted tangent bundles for general free rational curves is controlled by a finite set of data. We then apply our work to analyze Peyre’s “freeness” formulation of Manin’s Conjecture in the setting of rational curves. 
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  2. ; ; (, Osaka mathematical journal)
    Free, publicly-accessible full text available January 1, 2026
  3. ; ; ; (, Transactions of the American Mathematical Society)
    Full Text Available 
  4. ; ; ; (, Advances in Mathematics)
    Full Text Available 
  5. ; (, Proceedings of the London Mathematical Society)
    Full Text Available 
  6. ; (, Forum of mathematics Sigma)
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