scholarly journals The Noether–Lefschetz Theorem Via Vanishing of Coherent Cohomology

2008 ◽  
Vol 51 (2) ◽  
pp. 283-290 ◽  
Author(s):  
G. V. Ravindra
Keyword(s):  
Picard Number ◽  
Generic Hypersurface ◽  
Lefschetz Theorem

AbstractWe prove that for a generic hypersurface in ℙ2n+1 of degree at least 2 + 2/n, the n-th Picard number is one. The proof is algebraic in nature and follows from certain coherent cohomology vanishing.

scholarly journals The Noether–Lefschetz locus of surfaces in toric threefolds

2018 ◽  
Vol 20 (05) ◽  
pp. 1750070 ◽  
Author(s):  
Ugo Bruzzo ◽  
Antonella Grassi
Keyword(s):  
Linear System ◽  
Cartier Divisor ◽  
Ambient Space ◽  
Rational Curve ◽  
Ample Divisor ◽  
Smooth Surfaces ◽  
Picard Number ◽  
Lefschetz Theorem ◽  
Suitable Sense ◽  
General Surface

The Noether–Lefschetz theorem asserts that any curve in a very general surface [Formula: see text] in [Formula: see text] of degree [Formula: see text] is a restriction of a surface in the ambient space, that is, the Picard number of [Formula: see text] is [Formula: see text]. We proved previously that under some conditions, which replace the condition [Formula: see text], a very general surface in a simplicial toric threefold [Formula: see text] (with orbifold singularities) has the same Picard number as [Formula: see text]. Here we define the Noether–Lefschetz loci of quasi-smooth surfaces in [Formula: see text] in a linear system of a Cartier ample divisor with respect to a [Formula: see text]-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.

scholarly journals Rank two aCM bundles on the del Pezzo threefold with Picard number 3

2015 ◽  
Vol 429 ◽  
pp. 413-446 ◽  
Author(s):  
Gianfranco Casnati ◽  
Daniele Faenzi ◽  
Francesco Malaspina
Keyword(s):  
Picard Number ◽  
Del Pezzo ◽  
Acm Bundles

The Lefschetz Theorem on Hyperplane Sections

1959 ◽  
Vol 69 (3) ◽  
pp. 713 ◽  
Author(s):  
Aldo Andreotti ◽  
Theodore Frankel
Keyword(s):  
Lefschetz Theorem ◽  
Hyperplane Sections

scholarly journals K3 surfaces with Picard number three and canonical vector heights

2007 ◽  
Vol 76 (259) ◽  
pp. 1493-1499 ◽  
Author(s):  
Arthur Baragar ◽  
Ronald van Luijk
Keyword(s):  
K3 Surfaces ◽  
Picard Number ◽  
Canonical Vector

scholarly journals Seshadri constants on surfaces with Picard number 1

2016 ◽  
Vol 153 (3-4) ◽  
pp. 535-543
Author(s):  
Krishna Hanumanthu
Keyword(s):  
Picard Number ◽  
Seshadri Constants

Noether-Lefschetz theorem

1990 ◽  
Vol 60 (2) ◽  
pp. 465-472 ◽  
Author(s):  
Xian Wu
Keyword(s):  
Lefschetz Theorem

Generic hypersurface singularities

1997 ◽  
Vol 107 (2) ◽  
pp. 139-154 ◽  
Author(s):  
James Alexander ◽  
André Hirschowitz
Keyword(s):  
Generic Hypersurface ◽  
Hypersurface Singularities

scholarly journals NEW EXAMPLES OF CALABI–YAU 3-FOLDS AND GENUS ZERO SURFACES

2014 ◽  
Vol 16 (02) ◽  
pp. 1350010 ◽  
Author(s):  
GILBERTO BINI ◽  
FILIPPO F. FAVALE ◽  
JORGE NEVES ◽  
ROBERTO PIGNATELLI
Keyword(s):  
Fundamental Group ◽  
Moduli Space ◽  
General Type ◽  
Picard Number ◽  
Surfaces Of General Type ◽  
Geometric Genus ◽  
Genus Zero ◽  
New Family ◽  
Hodge Numbers ◽  
Projective Lines

We classify the subgroups of the automorphism group of the product of four projective lines admitting an invariant anticanonical smooth divisor on which the action is free. As a first application, we describe new examples of Calabi–Yau 3-folds with small Hodge numbers. In particular, the Picard number is 1 and the number of moduli is 5. Furthermore, the fundamental group is nontrivial. We also construct a new family of minimal surfaces of general type with geometric genus zero, K2 = 3 and fundamental group of order 16. We show that this family dominates an irreducible component of dimension 4 of the moduli space of the surfaces of general type.

scholarly journals Cox rings of K3 surfaces of Picard number three

2021 ◽  
Vol 565 ◽  
pp. 598-626
Author(s):  
Michela Artebani ◽  
Claudia Correa Deisler ◽  
Antonio Laface
Keyword(s):  
K3 Surfaces ◽  
Picard Number ◽  
Cox Rings
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