RT Journal Article
T1 Osculation for conic fibrations.
A1 Lanteri, Antonio
A1 Mallavibarrena Martínez de Castro, Raquel
AB 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 >= 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 is given. The case k = 3 for del Pezzo surfaces is also discussed, completing the analysis done for k = 2 in a previous paper by the authors (2001). Moreover, for conic fibrations X subset of 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
PB Elsevier Science
SN 0022-4049
YR 2016
FD 2016
LK https://hdl.handle.net/20.500.14352/24468
UL https://hdl.handle.net/20.500.14352/24468
LA eng
NO PRIN Geometry of Algebraic Varieties
NO University of Milano (FUR)
NO Spanish Ministry of Economy and Competitiveness
DS Docta Complutense
RD 6 abr 2025