scholarly journals G2-manifolds from K3 surfaces with non-symplectic automorphisms

2012 ◽  
Vol 62 (11) ◽  
pp. 2214-2226 ◽  
Author(s):  
Max Pumperla ◽  
Frank Reidegeld
Keyword(s):  
K3 Surfaces ◽  
G2 Manifolds ◽  
Symplectic Automorphisms

scholarly journals K3 surfaces with non-symplectic involution and compact irreducible G2-manifolds

2011 ◽  
Vol 151 (2) ◽  
pp. 193-218 ◽  
Author(s):  
ALEXEI KOVALEV ◽  
NAM-HOON LEE
Keyword(s):  
Betti Numbers ◽  
Matching Condition ◽  
K3 Surfaces ◽  
Connected Sum ◽  
Fano Threefolds ◽  
New Class ◽  
Blowing Up ◽  
G2 Manifolds

AbstractWe consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G2 developed by the first named author. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors and the latter K3 surfaces should satisfy a certain ‘matching condition’ intertwining on their periods and Kähler classes. Suitable examples of threefolds were previously obtained by blowing up curves in Fano threefolds.In this paper, we give a large new class of suitable algebraic threefolds using theory of K3 surfaces with non-symplectic involution due to Nikulin. These threefolds are not obtainable from Fano threefolds as above, and admit matching pairs leading to topologically new examples of compact irreducible G2-manifolds. ‘Geography’ of the values of Betti numbers b2, b3 for the new (and previously known) examples of irreducible G2 manifolds is also discussed.

scholarly journals Non-symplectic automorphisms of order 3 on K3 surfaces

2008 ◽  
Vol 342 (4) ◽  
pp. 903-921 ◽  
Author(s):  
Michela Artebani ◽  
Alessandra Sarti
Keyword(s):  
K3 Surfaces ◽  
Symplectic Automorphisms

scholarly journals Order eight non-symplectic automorphisms on elliptic K3 surfaces

2018 ◽  
Vol 116 ◽  
pp. 11-24 ◽  
Author(s):  
Dima Al Tabbaa ◽  
Alessandra Sarti
Keyword(s):  
K3 Surfaces ◽  
Symplectic Automorphisms

scholarly journals On symplectic and non-symplectic automorphisms of K3 surfaces

2013 ◽  
Vol 29 (1) ◽  
pp. 135-162 ◽  
Author(s):  
Alice Garbagnati ◽  
Alessandra Sarti
Keyword(s):  
K3 Surfaces ◽  
Symplectic Automorphisms
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