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EnglishThe 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]
| Titolo: | The Noether–Lefschetz locus of surfaces in toric threefolds | |
| Autori: | Bruzzo, Ugo; Grassi, Antonella | |
| Rivista: | ||
| Data di pubblicazione: | 2018 | |
| Volume: | 20 | |
| Fascicolo: | 5 | |
| Pagina iniziale: | 1 | |
| Pagina finale: | 20 | |
| Numero di Articolo: | 1750070 | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1142/S0219199717500705 | |
| URL: | https://arxiv.org/abs/1508.01895 | |
| Appare nelle tipologie: | 1.1 Journal article |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| Bruzzo-Grassi-CCM-WS.pdf | Versione Editoriale (PDF) | Non specificato | Administrator Richiedi una copia | |
| BruzzoGrassi-CCM.pdf | Documento in Post-print | Non specificato | Open Access Visualizza/Apri |
http://hdl.handle.net/20.500.11767/63911
