scholarly journals K3 Surfaces Over Number Fields with Geometric Picard Number One

2004 ◽  
pp. 135-140 ◽  
Author(s):  
Jordan S. Ellenberg
Keyword(s):  
Number Fields ◽  
K3 Surfaces ◽  
Picard Number

scholarly journals On the Picard number of K3 surfaces over number fields

2014 ◽  
Vol 8 (1) ◽  
pp. 1-17 ◽  
Author(s):  
François Charles
Keyword(s):  
Number Fields ◽  
K3 Surfaces ◽  
Picard Number

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 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

scholarly journals On the Supersingular Reduction of K3 Surfaces with Complex Multiplication

2018 ◽  
Vol 2020 (20) ◽  
pp. 7306-7346
Author(s):  
Kazuhiro Ito
Keyword(s):  
Comparison Theorem ◽  
Complex Multiplication ◽  
K3 Surfaces ◽  
Explicit Description ◽  
Brauer Group ◽  
K3 Surface ◽  
Good Reduction ◽  
Picard Number ◽  
Reduction Modulo ◽  
Modulo P

Abstract We study the good reduction modulo $p$ of $K3$ surfaces with complex multiplication. If a $K3$ surface with complex multiplication has good reduction, we calculate the Picard number and the height of the formal Brauer group of the reduction. Moreover, if the reduction is supersingular, we calculate its Artin invariant under some assumptions. Our results generalize some results of Shimada for $K3$ surfaces with Picard number $20$. Our methods rely on the main theorem of complex multiplication for $K3$ surfaces by Rizov, an explicit description of the Breuil–Kisin modules associated with Lubin–Tate characters due to Andreatta, Goren, Howard, and Madapusi Pera, and the integral comparison theorem recently established by Bhatt, Morrow, and Scholze.

K3-surfaces with Picard number 2

1988 ◽  
Vol 50 (1) ◽  
pp. 73-82 ◽  
Author(s):  
Joachim Wehler
Keyword(s):  
K3 Surfaces ◽  
Picard Number

On K3 surfaces with large Picard number

1984 ◽  
Vol 75 (1) ◽  
pp. 105-121 ◽  
Author(s):  
D. R. Morrison
Keyword(s):  
K3 Surfaces ◽  
Picard Number

scholarly journals HIGHER RANK BRILL–NOETHER THEORY ON SECTIONS OF K3 SURFACES

2012 ◽  
Vol 23 (07) ◽  
pp. 1250075 ◽  
Author(s):  
GAVRIL FARKAS ◽  
ANGELA ORTEGA
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Moduli Space Of Curves ◽  
Picard Number ◽  
Detailed Proof ◽  
Rank 2 ◽  
Higher Rank

We discuss the role of K3 surfaces in the context of Mercat's conjecture in higher rank Brill–Noether theory. Using liftings of Koszul classes, we show that Mercat's conjecture in rank 2 fails for any number of sections and for any gonality stratum along a Noether–Lefschetz divisor inside the locus of curves lying on K3 surfaces. Then we show that Mercat's conjecture in rank 3 fails even for curves lying on K3 surfaces with Picard number 1. Finally, we provide a detailed proof of Mercat's conjecture in rank 2 for general curves of genus 11, and describe explicitly the action of the Fourier–Mukai involution on the moduli space of curves.

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