scholarly journals Real representatives of equisingular strata of simple quartic surfaces

2019 ◽  
Vol 30 (12) ◽  
pp. 1950063
Author(s):  
Çi̇sem Güneş Aktaş
Keyword(s):  
Quartic Surfaces

We develop an algorithm detecting real representatives in equisingular strata of projective models of [Formula: see text]-surfaces. We apply this algorithm to spatial quartics and find two new examples of real strata without real representatives. As a by-product, we also give a new proof for the only previously known example of plane sextics.

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.

Supersingular quartic surfaces

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

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
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