The Noether–Lefschetz locus of surfaces in toric threefolds

DOI10.1142/S0219199717500705zbMath1423.14053arXiv1508.01895OpenAlexW2962744992MaRDI QIDQ3177298

Antonella Grassi, Ugo Bruzzo

Publication date: 30 July 2018

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.01895

zbMATH Keywords

Castelnuovo-Mumford regularityhypersurfacesHilbert schemesNoether-Lefschetz locusOda's conjecturesimplicial toric varietiessingular threefoldsZariski and Kähler differentials

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Picard groups (14C22) Hypersurfaces and algebraic geometry (14J70)

Related Items

Existence and Density of General Components of the Noether–Lefschetz Locus on Normal Threefolds, Small codimension components of the Hodge locus containing the Fermat variety, The Noether–Lefschetz theorem in arbitrary characteristic, On the codimension of Noether–Lefschetz loci for toric threefolds, On the Hodge conjecture for quasi-smooth intersections in toric varieties, Codimension bounds for the Noether-Lefschetz components for toric varieties, Algebraic hyperbolicity for surfaces in toric threefolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Koszul cohomology and the geometry of projective varieties. II
• Toric Calabi-Yau hypersurfaces fibered by weighted \(K3\) hypersurfaces
• Subvarieties of generic hypersurfaces in a nonsingular projective toric variety
• A new proof of the explicit Noether-Lefschetz theorem
• On the Hodge structure of projective hypersurfaces in toric varieties
• Une précision concernant le théorème de Noether. (A precision concerning the theorem of Noether)
• Semiample hypersurfaces in toric varieties
• Torsion and cotorsion in the sheaf of Kähler differentials on some mild singularities
• Composantes de petite codimension du lieu de Noether-Lefschetz. (Small codimension components of the Noether-Lefschetz locus)
• The Noether-Lefschetz theorem for the divisor class group
• PICARD GROUP OF HYPERSURFACES IN TORIC 3-FOLDS
• Deformations of Algebraic Schemes
• Vanishing Theorems, A Theorem of Severi, and the Equations Defining Projective Varieties
• Composantes de petite codimension du lieu de Noether-Lefschetz: Un argument asymptotique en faveur de la conjecture de Hodge pour les hypersurfaces
• A characterization of Gorenstein toric Fano $n$-folds with index $n$ and Fujita's conjecture
• Explicit Noether–Lefschetz for arbitrary threefolds
• Cohomology of rational forms and a vanishing theorem on toric varieties
• Differentials on Quotients of Algebraic Varieties