The Noether-Lefschetz theorem asserts that any curve in a very general surface (Formula presented.) in (Formula presented.) of degree (Formula presented.) is a restriction of a surface in the ambient space, that is, the Picard number of (Formula presented.) is (Formula presented.). We proved previously that under some conditions, which replace the condition (Formula presented.), a very general surface in a simplicial toric threefold (Formula presented.) (with orbifold singularities) has the same Picard number as (Formula presented.). Here we define the Noether-Lefschetz loci of quasi-smooth surfaces in (Formula presented.) in a linear system of a Cartier ample divisor with respect to a (Formula presented.)-regular, respectively 0-regular, ample Cartier divisor, and give bounds on their codimensions. We also study the components of the Noether-Lefschetz loci which contain a line, defined as a rational curve which is minimal in a suitable sense.
The Noether–Lefschetz locus of surfaces in toric threefolds / Bruzzo, Ugo; Grassi, Antonella. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 20:5(2017).
|Titolo:||The Noether–Lefschetz locus of surfaces in toric threefolds|
|Autori:||Bruzzo, Ugo; Grassi, Antonella|
|Data di pubblicazione:||2017|
|Numero di Articolo:||1750070|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1142/S0219199717500705|
|Appare nelle tipologie:||1.1 Journal article|