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(2018), pp. 1-20. [10.1142/S0219199717500705]

The Noether–Lefschetz locus of surfaces in toric threefolds

Bruzzo, Ugo
Membro del Collaboration group
;
2018

Abstract

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.
20
5
1
20
1750070
https://arxiv.org/abs/1508.01895
Bruzzo, Ugo; Grassi, Antonella
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/63911
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