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. LanteriPrimo
;
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.
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Rational conic fibrations containing special curves transverse to the fibers.pdf
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