Rational conic fibrations embedded in P^N and containing an irreducible curve C transverse to the fibers are classified when C is either a plane curve or a rational normal curve of any degree d. This extends our previous results concerning lines, conics and twisted cubics. To emphasize the role of linear normality, the case in which C is a nonnormal rational quartic is also discussed. Moreover, the rank of the d-th jet map of the surface at all points lying on such curves is evaluated.

Rational conic fibrations containing special curves transverse to the fibers / A. Lanteri, R. Mallavibarrena. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - (2024), pp. 1-20. [Epub ahead of print] [10.1080/00927872.2024.2393693]

Rational conic fibrations containing special curves transverse to the fibers

A. Lanteri
Primo
;
2024

Abstract

Rational conic fibrations embedded in P^N and containing an irreducible curve C transverse to the fibers are classified when C is either a plane curve or a rational normal curve of any degree d. This extends our previous results concerning lines, conics and twisted cubics. To emphasize the role of linear normality, the case in which C is a nonnormal rational quartic is also discussed. Moreover, the rank of the d-th jet map of the surface at all points lying on such curves is evaluated.
conic fibration (rational); plane curve; rational normal curve; osculation
Settore MATH-02/B - Geometria
2024
3-set-2024
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1119461
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