scholarly journals Construction of singular rational surfaces of Picard number one with ample canonical divisor

2012 ◽  
Vol 140 (6) ◽  
pp. 1865-1879 ◽  
Author(s):  
DongSeon Hwang ◽  
JongHae Keum
Keyword(s):  
Picard Number ◽  
Canonical Divisor ◽  
Rational Surfaces

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 surfaces whose prime-sections contain a

1934 ◽  
Vol 30 (2) ◽  
pp. 170-177 ◽  
Author(s):  
J. Bronowski
Keyword(s):  
Hyperelliptic Curves ◽  
Ruled Surfaces ◽  
Minimum Order ◽  
Rational Surfaces ◽  
Pencil Of Conics

The surfaces whose prime-sections are hyperelliptic curves of genus p have been classified by G. Castelnuovo. If p > 1, they are the surfaces which contain a (rational) pencil of conics, which traces the on the prime-sections. Thus, if we exclude ruled surfaces, they are rational surfaces. The supernormal surfaces are of order 4p + 4 and lie in space [3p + 5]. The minimum directrix curve to the pencil of conics—that is, the curve of minimum order which meets each conic in one point—may be of any order k, where 0 ≤ k ≤ p + 1. The prime-sections of these surfaces are conveniently represented on the normal rational ruled surfaces, either by quadric sections, or by quadric sections residual to a generator, according as k is even or odd.

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

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 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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