On the Geometry of Conic Bundles Arising in Adjunction Theory

2009 ◽  
Vol 160 (1) ◽  
pp. 223-251 ◽  
Author(s):  
Gian Mario Besana
Keyword(s):  
Adjunction Theory ◽  
Conic Bundles

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.

scholarly journals Effective adjunction theory

2018 ◽  
Vol 64 (2) ◽  
pp. 243-257 ◽  
Author(s):  
Marco Andreatta ◽  
Claudio Fontanari
Keyword(s):  
Adjunction Theory

scholarly journals ADJUNCTION FOR VARIETIES WITH A ℂ* ACTION

2020 ◽  
Author(s):  
ELEONORA A. ROMANO ◽  
JAROSŁAW A. WIŚNIEWSKI
Keyword(s):  
Fixed Point ◽  
Line Bundle ◽  
Normal Bundle ◽  
Ample Line Bundle ◽  
Projective Manifold ◽  
Fano Manifolds ◽  
Adjunction Theory ◽  
Rank 2 ◽  
General Orbit ◽  
Complex Projective

Abstract Let X be a complex projective manifold, L an ample line bundle on X, and assume that we have a ℂ* action on (X;L). We classify such triples (X; L;ℂ*) for which the closure of a general orbit of the ℂ* action is of degree ≤ 3 with respect to L and, in addition, the source and the sink of the action are isolated fixed points, and the ℂ* action on the normal bundle of every fixed point component has weights ±1. We treat this situation by relating it to the classical adjunction theory. As an application, we prove that contact Fano manifolds of dimension 11 and 13 are homogeneous if their group of automorphisms is reductive of rank ≥ 2.

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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