scholarly journals Functional transcendence for the unipotent Albanese map

2021 ◽  
Vol 15 (6) ◽  
pp. 1565-1580
Author(s):  
Daniel Rayor Hast
Keyword(s):  
Albanese Map

scholarly journals A Pair of Rigid Surfaces with pg= q = 2 and K2= 8 Whose Universal Cover is Not the Bidisk

2018 ◽  
Vol 2020 (11) ◽  
pp. 3453-3493
Author(s):  
Francesco Polizzi ◽  
Carlos Rito ◽  
Xavier Roulleau
Keyword(s):  
Minimal Surfaces ◽  
Universal Cover ◽  
The Family ◽  
Albanese Map ◽  
Rigid Surfaces

Abstract We construct two complex-conjugated rigid minimal surfaces with $p_g\!=q=2$ and $K^2\!=8$ whose universal cover is not biholomorphic to the bidisk $\mathbb{H} \times \mathbb{H}$. We show that these are the unique surfaces with these invariants and Albanese map of degree 2, apart from the family of product-quotient surfaces given in [33]. This completes the classification of surfaces with $p_g=q=2, K^2=8$, and Albanese map of degree 2.

scholarly journals The l-component of the unipotent Albanese map

2007 ◽  
Vol 340 (1) ◽  
pp. 223-235 ◽  
Author(s):  
Minhyong Kim ◽  
Akio Tamagawa
Keyword(s):  
Albanese Map

On the structure of generalized Albanese varieties

1992 ◽  
Vol 111 (2) ◽  
pp. 267-272
Author(s):  
Hurit nsiper
Keyword(s):  
Algebraic Group ◽  
Class Group ◽  
Effective Divisor ◽  
Closed Field ◽  
Projective Surface ◽  
Mapping Property ◽  
Rational Map ◽  
Algebraically Closed Field ◽  
Albanese Map ◽  
Albanese Variety

Given a smooth projective surface X over an algebraically closed field k and a modulus (an effective divisor) m on X, one defines the idle class group Cm(X) of X with modulus m (see 1, chapter III, section 4). The corresponding generalized Albanese variety Gum and the generalized Albanese map um:X|m|Gum have the following universal mapping property (2): if :XG is a rational map into a commutative algebraic group which induces a homomorphism Cm(X)G(k) (1, chapter III, proposition 1), then factors uniquely through um.

scholarly journals A new family of surfaces with p g =q =2 and K 2 =6 whose Albanese map has degree 4

2014 ◽  
Vol 90 (3) ◽  
pp. 741-762 ◽  
Author(s):  
Matteo Penegini ◽  
Francesco Polizzi
Keyword(s):  
New Family ◽  
Albanese Map
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