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Interpolation of rational scrolls

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arxiv 2111.02466 v1 pith:73O2DA6A submitted 2021-11-03 math.AG

Ziv Ran This is my paper · ORCID
classification math.AG
keywords scrollsbalancedexistrationaltherecasescontaindegree
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abstract

We show in many cases that there exist rational scrolls which are balanced, i.e. they contain the expected number of general linear spaces as rulings. For example, there exist balanced scrolls of degree $mk+1$ and fibre dimension $k$ in $\P^{2k+1}$ for all $m\geq 1$.

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  1. Restricted tangent bundle of rational curves on projective hypersurfaces

    math.AG 2025-07 conditional novelty 7.0 of 10

    A general Fano hypersurface of degree d in P^n has rational curves of degree e with balanced restricted tangent bundle exactly when e exceeds (n-1)/(n+1-d), and quadrics have a separate parity rule.

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