scholarly journals A higher Albanese map for complex threefolds based on a construction by M. Green

2005 ◽  
Vol 186 (2) ◽  
pp. 111-146
Author(s):  
Lorenz Schneider
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

scholarly journals PSEUDO-EFFECTIVE LINE BUNDLES ON COMPACT KÄHLER MANIFOLDS

2001 ◽  
Vol 12 (06) ◽  
pp. 689-741 ◽  
Author(s):  
JEAN-PIERRE DEMAILLY ◽  
THOMAS PETERNELL ◽  
MICHAEL SCHNEIDER
Keyword(s):  
Line Bundle ◽  
Vector Bundles ◽  
Kähler Manifolds ◽  
Line Bundles ◽  
Kahler Manifolds ◽  
Ideal Sheaf ◽  
Multiplier Ideal Sheaf ◽  
Albanese Map ◽  
Multiplier Ideal ◽  
Hard Lefschetz Theorem

The goal of this work is to pursue the study of pseudo-effective line bundles and vector bundles. Our first result is a generalization of the Hard Lefschetz theorem for cohomology with values in a pseudo-effective line bundle. The Lefschetz map is shown to be surjective when (and, in general, only when) the pseudo-effective line bundle is twisted by its multiplier ideal sheaf. This result has several geometric applications, e.g. to the study of compact Kähler manifolds with pseudo-effective canonical or anti-canonical line bundles. Another concern is to understand pseudo-effectivity in more algebraic terms. In this direction, we introduce the concept of an "almost" nef line bundle, and mean by this that the degree of the bundle is nonnegative on sufficiently generic curves. It can be shown that pseudo-effective line bundles are almost nef, and our hope is that the converse also holds true. This can be checked in some cases, e.g. for the canonical bundle of a projective 3-fold. From this, we derive some geometric properties of the Albanese map of compact Kähler 3-folds.

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