Supersingular quartic surfaces

2019 ◽  
Vol 223 (11) ◽  
pp. 4701-4707
Author(s):  
Junmyeong Jang
Keyword(s):  
Quartic Surfaces

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

COUNTEREXAMPLES TO THE HASSE PRINCIPLE IN FAMILIES

2021 ◽  
pp. 1-10
Author(s):  
NGUYEN XUAN THO
Keyword(s):  
Hasse Principle ◽  
Quartic Surfaces

Abstract We generalise two quartic surfaces studied by Swinnerton-Dyer to give two infinite families of diagonal quartic surfaces which violate the Hasse principle. Standard calculations of Brauer–Manin obstructions are exhibited.

scholarly journals AT MOST 64 LINES ON SMOOTH QUARTIC SURFACES (CHARACTERISTIC 2)

2017 ◽  
Vol 232 ◽  
pp. 76-95
Author(s):  
SŁAWOMIR RAMS ◽  
MATTHIAS SCHÜTT
Keyword(s):  
Geometric Proof ◽  
Characteristic 2 ◽  
Quartic Surfaces

Let $k$ be a field of characteristic $2$. We give a geometric proof that there are no smooth quartic surfaces $S\subset \mathbb{P}_{k}^{3}$ with more than 64 lines (predating work of Degtyarev which improves this bound to 60). We also exhibit a smooth quartic containing 60 lines which thus attains the record in characteristic $2$.

On classification of cubic and quartic surfaces

2004 ◽  
Author(s):  
Vladimir M. Degtyarev ◽  
Ivan P. Krylov
Keyword(s):  
Quartic Surfaces

scholarly journals A type of periodicity of certain quartic surfaces

1942 ◽  
Vol 7 (1) ◽  
pp. 73-80 ◽  
Author(s):  
W. L. Edge
Keyword(s):  
Present Note ◽  
Quartic Surface ◽  
Periodic Property ◽  
A Chain ◽  
Quartic Surfaces ◽  
Do So

The following pages have been written in consequence of reading some paragraphs by Reye, in which he obtains, from a quartic surface, a chain of contravariant quartic envelopes and of covariant quartic loci. This chain is, in general, unending; but Reye at once foresaw the possibility of the quartic surface being such that the chain would be periodic. The only example which he gave of periodicity being realised was that in which the quartic surface was a repeated quadric. It is reasonable to suppose that, had he been able to do so, he would have chosen some surface which had the periodic property without being degenerate; in the present note two such surfaces are signalised.

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