The period-index problem for the Brauer group of an algebraic surface

2004 ◽  
Vol 123 (1) ◽  
pp. 71-94 ◽  
Author(s):  
A. J. de Jong
Keyword(s):  
Algebraic Surface ◽  
Brauer Group ◽  
Index Problem

scholarly journals Failure of the Hasse principle on general surfaces

2013 ◽  
Vol 12 (4) ◽  
pp. 853-877 ◽  
Author(s):  
Brendan Hassett ◽  
Anthony Várilly-Alvarado
Keyword(s):  
Algebraic Surface ◽  
Hodge Theory ◽  
Double Cover ◽  
Hasse Principle ◽  
Brauer Group

AbstractWe show that transcendental elements of the Brauer group of an algebraic surface can obstruct the Hasse principle. We construct a general $K 3$ surface $X$ of degree $2$ over $ \mathbb{Q} $, together with a 2-torsion Brauer class $\alpha $ that is unramified at every finite prime, but ramifies at real points of $X$. With motivation from Hodge theory, the pair $(X, \alpha )$ is constructed from a double cover of ${ \mathbb{P} }^{2} \times { \mathbb{P} }^{2} $ ramified over a hypersurface of bidegree $(2, 2)$.

scholarly journals Isotopic triangulation of a real algebraic surface

2009 ◽  
Vol 44 (9) ◽  
pp. 1291-1310 ◽  
Author(s):  
Lionel Alberti ◽  
Bernard Mourrain ◽  
Jean-Pierre Técourt
Keyword(s):  
Algebraic Surface ◽  
Real Algebraic Surface

scholarly journals On the Reconstruction of the Center of a Projection by Distances and Incidence Relations

2020 ◽  
Author(s):  
András Pongrácz ◽  
Csaba Vincze
Keyword(s):  
Algebraic Surface ◽  
Basic Problem ◽  
Rotational Symmetry ◽  
Image Plane ◽  
Equivalent Condition ◽  
Central Projection ◽  
Profile Curve ◽  
Reconstruction Process ◽  
Restricted Area ◽  
Photographic Images

AbstractUp to an orientation-preserving symmetry, photographic images are produced by a central projection of a restricted area in the space into the image plane. To obtain reliable information about physical objects and the environment through the process of recording is the basic problem of photogrammetry. We present a reconstruction process based on distances from the center of projection and incidence relations among the points to be projected. For any triplet of collinear points in the space, we construct a surface of revolution containing the center of the projection. It is a generalized conic that can be represented as an algebraic surface. The rotational symmetry allows us to restrict the investigations to the defining polynomial of the profile curve in the image plane. An equivalent condition for the boundedness is given in terms of the input parameters, and it is shown that the defining polynomial of the profile curve is irreducible.

scholarly journals The topological period–index problem over 8‐complexes, I

2019 ◽  
Vol 12 (4) ◽  
pp. 1368-1395 ◽  
Author(s):  
Xing Gu
Keyword(s):  
Index Problem

scholarly journals The inverse Wiener polarity index problem for chemical trees

PLoS ONE ◽  
2018 ◽  
Vol 13 (5) ◽  
pp. e0197142 ◽  
Author(s):  
Zhibin Du ◽  
Akbar Ali
Keyword(s):  
Polarity Index ◽  
Index Problem ◽  
Chemical Trees

scholarly journals On the Brauer group of diagonal quartic surfaces

2011 ◽  
Vol 83 (3) ◽  
pp. 659-672 ◽  
Author(s):  
Evis Ieronymou ◽  
Alexei N. Skorobogatov ◽  
Yuri G. Zarhin
Keyword(s):  
Brauer Group ◽  
Quartic Surfaces
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