Data di Pubblicazione:
2016
Citazione:
Osculation for conic fibrations / A. Lanteri, R. Mallavibarrena. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 220:8(2016 Feb), pp. 2852-2878. [10.1016/j.jpaa.2016.01.005]
Abstract:
Smooth projective surfaces fibered in conics over a smooth curve are investigated with respect to their k-th osculatory behavior.
Due to the bound for the dimension of their osculating spaces they do not differ at all from a general surface
for k=2, while their structure plays a significant role for k \geq 3. The dimension of the
osculating space at any point is studied taking into account the possible existence of curves of low degree
transverse to the fibers, and several examples are discussed to illustrate concretely the various situations
arising in this analysis. As an application, a complete description of the osculatory behavior of
Castelnuovo surfaces, i.e. rational surfaces whose hyperplane sections correspond to a linear system of nodal quartic plane curves.
is given. The case k=3 for del Pezzo surfaces is also discussed, completing the analysis done for k=2$ i
a previous paper of the authors (2001).
Moreover, for conic fibrations X in P^N, whose k-th inflectional locus
has the expected codimension a precise description of this locus is provided in terms of Chern classes.
In particular, for N=8, it turns out that either X is hypo-osculating for k=3, or its third inflectional locus is 1-dimensional.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
conic fibration; inflectional locus; k-jet, del Pezzo surface; Castelnuovo surface
Elenco autori:
A. Lanteri, R. Mallavibarrena
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