scholarly journals The rationality problem for conic bundles

2018 ◽  
Vol 73 (3) ◽  
pp. 375-456 ◽  
Author(s):  
Yu. G. Prokhorov
Keyword(s):  
Conic Bundles ◽  
Rationality Problem

On the rationality problem for conic bundles

1987 ◽  
Vol 54 (2) ◽  
pp. 271-294 ◽  
Author(s):  
V. A. Iskovskikh
Keyword(s):  
Conic Bundles ◽  
Rationality Problem

scholarly journals Rationality problem for norm one tori in small dimensions

2019 ◽  
Vol 89 (322) ◽  
pp. 923-940 ◽  
Author(s):  
Sumito Hasegawa ◽  
Akinari Hoshi ◽  
Aiichi Yamasaki
Keyword(s):  
Rationality Problem

scholarly journals Geometrically rational real conic bundles and very transitive actions

2010 ◽  
Vol 147 (1) ◽  
pp. 161-187 ◽  
Author(s):  
Jérémy Blanc ◽  
Frédéric Mangolte
Keyword(s):  
Automorphism Groups ◽  
Algebraic Surfaces ◽  
Algebraic Models ◽  
Transitive Automorphism ◽  
Real Locus ◽  
Real Algebraic Surfaces ◽  
Conic Bundles ◽  
Transitive Actions ◽  
Insight Into

AbstractIn this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

The rationality problem for semisimple group varieties

1998 ◽  
Vol 1998 (504) ◽  
pp. 1-28 ◽  
Author(s):  
Vladimir P. Platonov ◽  
Vladimir I. Chernousov
Keyword(s):  
Semisimple Group ◽  
Rationality Problem

COUNTING MULTISECTIONS IN CONIC BUNDLES OVER A CURVE DEFINED OVER 𝔽q

2011 ◽  
Vol 07 (06) ◽  
pp. 1663-1680
Author(s):  
SEYFI TÜRKELLI
Keyword(s):  
Function Field ◽  
Algebraic Numbers ◽  
Conic Bundle ◽  
Conic Bundles ◽  
Special Case

For a given conic bundle X over a curve C defined over 𝔽q, we count irreducible branch covers of C in X of degree d and height e ≫ 1. As a special case, we get the number of algebraic numbers of degree d and height e over the function field 𝔽q(C).

scholarly journals STABILITY OF CONIC BUNDLES: WITH AN APPENDIX BY MUNDET I RIERA

2000 ◽  
Vol 11 (08) ◽  
pp. 1027-1055 ◽  
Author(s):  
TOMÁS L. GÓMEZ ◽  
IGNACIO SOLS
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Conic Bundle ◽  
Conic Bundles ◽  
Definition Of

Roughly speaking, a conic bundle is a surface, fibered over a curve, such that the fibers are conics (not necessarily smooth). We define stability for conic bundles and construct a moduli space. We prove that (after fixing some invariants) these moduli spaces are irreducible (under some conditions). Conic bundles can be thought of as generalizations of orthogonal bundles on curves. We show that in this particular case our definition of stability agrees with the definition of stability for orthogonal bundles. Finally, in an appendix by I. Mundet i Riera, a Hitchin-Kobayashi correspondence is stated for conic bundles.

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