scholarly journals Holomorphic Cartan geometries on complex tori

2018 ◽  
Vol 356 (3) ◽  
pp. 316-321
Author(s):  
Indranil Biswas ◽  
Sorin Dumitrescu
Keyword(s):  
Complex Tori ◽  
Cartan Geometries

scholarly journals Hodge modules on complex tori and generic vanishing for compact Kähler manifolds

2017 ◽  
Vol 21 (4) ◽  
pp. 2419-2460 ◽  
Author(s):  
Giuseppe Pareschi ◽  
Mihnea Popa ◽  
Christian Schnell
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Complex Tori ◽  
Generic Vanishing

scholarly journals Yang–Mills connections on compact complex tori

2015 ◽  
Vol 07 (02) ◽  
pp. 293-307
Author(s):  
Indranil Biswas
Keyword(s):  
Algebraic Group ◽  
Maximal Compact Subgroup ◽  
Compact Subgroup ◽  
Structure Group ◽  
Kähler Structure ◽  
Yang Mills ◽  
Complex Torus ◽  
Complex Tori

Let G be a connected reductive complex affine algebraic group and K ⊂ G a maximal compact subgroup. Let M be a compact complex torus equipped with a flat Kähler structure and (EG, θ) a polystable Higgs G-bundle on M. Take any C∞ reduction of structure group EK ⊂ EG to the subgroup K that solves the Yang–Mills equation for (EG, θ). We prove that the principal G-bundle EG is polystable and the above reduction EK solves the Einstein–Hermitian equation for EG. We also prove that for a semistable (respectively, polystable) Higgs G-bundle (EG, θ) on a compact connected Calabi–Yau manifold, the underlying principal G-bundle EG is semistable (respectively, polystable).

Cartan Geometries and their Symmetries

2016 ◽  
Author(s):  
Mike Crampin ◽  
David Saunders
Keyword(s):  
Cartan Geometries

scholarly journals A characterization of compact complex tori via automorphism groups

2013 ◽  
Vol 357 (3) ◽  
pp. 961-968 ◽  
Author(s):  
Baohua Fu ◽  
De-Qi Zhang
Keyword(s):  
Automorphism Groups ◽  
Complex Tori

scholarly journals Abelian varieties attached to cycles of intermediate dimension

1979 ◽  
Vol 75 ◽  
pp. 95-119 ◽  
Author(s):  
Hiroshi Saito
Keyword(s):  
Abelian Variety ◽  
Projective Variety ◽  
Classical Case ◽  
Degree Zero ◽  
Algebraic Construction ◽  
Jacobian Varieties ◽  
Codimension One ◽  
Picard Variety ◽  
Complex Tori ◽  
Intermediate Jacobian

The group of cycles of codimension one algebraically equivalent to zero of a nonsingular projective variety modulo rational equivalence forms an abelian variety, i.e., the Picard variety. To the group of cycles of dimension zero and of degree zero, there corresponds an abelian variety, the Albanese variety. Similarly, Weil, Lieberman and Griffiths have attached complex tori to the cycles of intermediate dimension in the classical case. The aim of this article is to give a purely algebraic construction of such “intermediate Jacobian varieties.”

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