On the picard group and the brauer group of a real algebraic surface

2000 ◽  
Vol 67 (2) ◽  
pp. 168-175
Author(s):  
V. A. Krasnov
Keyword(s):  
Algebraic Surface ◽  
Picard Group ◽  
Brauer Group ◽  
Real Algebraic Surface

The Brauer group of a noncomplete real algebraic surface

2000 ◽  
Vol 67 (3) ◽  
pp. 296-300 ◽  
Author(s):  
V. A. Krasnov
Keyword(s):  
Algebraic Surface ◽  
Brauer Group ◽  
Real Algebraic Surface

On the Brauer group of a real algebraic surface

1996 ◽  
Vol 60 (6) ◽  
pp. 707-710
Author(s):  
V. A. Krasnov
Keyword(s):  
Algebraic Surface ◽  
Brauer Group ◽  
Real Algebraic Surface

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

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 Algorithmical determination of the topology of a real algebraic surface

2004 ◽  
Vol 38 (6) ◽  
pp. 1551-1567 ◽  
Author(s):  
E. Fortuna ◽  
P. Gianni ◽  
D. Luminati
Keyword(s):  
Algebraic Surface ◽  
Real Algebraic Surface

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 Generalised Thurston-Bennequin invariants for real algebraic surface singularities

2005 ◽  
Vol 117 (3) ◽  
pp. 273-298 ◽  
Author(s):  
Ferit Öztürk
Keyword(s):  
Algebraic Surface ◽  
Surface Singularities ◽  
Real Algebraic Surface

Analogues of the Harnack-Thom inequality for a real algebraic surface

2000 ◽  
Vol 64 (5) ◽  
pp. 915-937
Author(s):  
Vyacheslav A Krasnov
Keyword(s):  
Algebraic Surface ◽  
Real Algebraic Surface

scholarly journals The adjacency graph of a real algebraic surface

2005 ◽  
Vol 16 (5) ◽  
pp. 271-292 ◽  
Author(s):  
E. Fortuna ◽  
P. Gianni ◽  
D. Luminati ◽  
P. Parenti
Keyword(s):  
Algebraic Surface ◽  
Adjacency Graph ◽  
Real Algebraic Surface

Numerical roadmap of smooth bounded real algebraic surface

2020 ◽  
Vol 79 ◽  
pp. 101858
Author(s):  
Changbo Chen ◽  
Wenyuan Wu ◽  
Yong Feng
Keyword(s):  
Algebraic Surface ◽  
Real Algebraic Surface
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