This analysis shows how curves interpolate in Hirzebruch surfaces, suggesting limits on expected number of points.
When a≥2, we show that a general pointed curve never interpolates through the expected number of points in the Hirzebruch surface Hₐ, with one exception. In the exceptional case, the number of such interpolating maps is determined by the geometric Tevelev degrees of P¹, which have been previously computed.
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Cela et al. (2025) studied this question.
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