An asymptotic description of Noether-Lefschetz components in toric varieties
| dc.contributor.author | Bruzzo, Ugo | |
| dc.contributor.author | Montoya, William D. | |
| dc.date.accessioned | 2019-03-19T08:17:32Z | |
| dc.date.available | 2019-03-19T08:17:32Z | |
| dc.date.issued | 2019-03-19 | |
| dc.description.abstract | We extend the definition of Noether-Leschetz components to quasi-smooth hyper- surfaces in a projective toric variety PΣ2k+1 having orbifold singularities, and prove that asymptoticaly the components whose codimension is bounded from above are made of hy- persurfaces containing a small degree k-dimensional subvariety. As a corollary we get an asymptotic characterization of the components with small codimension, generalizing the work of Otwinowska for P2k+1 = P2k+1 and Green and Voisin for P2k+1 = P3. Some tools that are developed in the paper are a generalization of Macaulay’s theorem for Fano, irreducible normal varieties with rational singularieties, satisfying a suitable additional condition, and an extension of the notion of Gorenstein ideal for normal varieties with finetely generated Cox ring. | en_US |
| dc.identifier.uri | https://openscience.sissa.it/handle/1963/35331 | |
| dc.language.iso | en | en_US |
| dc.publisher | SISSA | en_US |
| dc.relation.ispartofseries | SISSA;08/2019/MATE | |
| dc.subject | Noether-Lefschetz locus | en_US |
| dc.subject | Picard number | en_US |
| dc.subject | toric varieties | en_US |
| dc.title | An asymptotic description of Noether-Lefschetz components in toric varieties | en_US |
| dc.type | Preprint | en_US |