scholarly journals On the rank of the fibers of rational elliptic surfaces

2012 ◽  
Vol 6 (7) ◽  
pp. 1289-1314
Author(s):  
Cecília Salgado
Keyword(s):  
Elliptic Surfaces ◽  
Rational Elliptic Surfaces

Extremal rational elliptic surfaces in characteristicp

1991 ◽  
Vol 207 (1) ◽  
pp. 429-437 ◽  
Author(s):  
William E. Lang
Keyword(s):  
Elliptic Surfaces ◽  
Rational Elliptic Surfaces

Arithmetic and geometry of rational elliptic surfaces

2016 ◽  
Vol 46 (6) ◽  
pp. 2061-2076
Author(s):  
Cec[! \' i!]lia Salgado
Keyword(s):  
Elliptic Surfaces ◽  
Rational Elliptic Surfaces

Rational Elliptic Surfaces

2019 ◽  
pp. 145-159
Author(s):  
Matthias Schütt ◽  
Tetsuji Shioda
Keyword(s):  
Elliptic Surfaces ◽  
Rational Elliptic Surfaces

scholarly journals Multiple fibers on rational elliptic surfaces

1988 ◽  
Vol 307 (1) ◽  
pp. 205-205 ◽  
Author(s):  
Brian Harbourne ◽  
William E. Lang
Keyword(s):  
Elliptic Surfaces ◽  
Multiple Fibers ◽  
Rational Elliptic Surfaces

scholarly journals Cox rings of extremal rational elliptic surfaces

2015 ◽  
Vol 368 (3) ◽  
pp. 1735-1757 ◽  
Author(s):  
Michela Artebani ◽  
Alice Garbagnati ◽  
Antonio Laface
Keyword(s):  
Elliptic Surfaces ◽  
Cox Rings ◽  
Rational Elliptic Surfaces

scholarly journals TOWARDS THE STANDARD MODEL SPECTRUM FROM ELLIPTIC CALABI–YAU MANIFOLDS

2004 ◽  
Vol 19 (12) ◽  
pp. 1987-2014 ◽  
Author(s):  
BJÖRN ANDREAS ◽  
GOTTFRIED CURIO ◽  
ALBRECHT KLEMM
Keyword(s):  
Standard Model ◽  
Global Section ◽  
Elliptic Surfaces ◽  
Spectral Cover ◽  
Elliptic Fiber ◽  
The Standard Model ◽  
Free Involution ◽  
Simply Connected ◽  
Rational Elliptic Surfaces ◽  
Standard Model Gauge Group

We show that it is possible to construct supersymmetric three-generation models with the Standard Model gauge group in the framework of non-simply-connected elliptically fibered Calabi–Yau threefolds, without section but with a bi-section. The fibrations on a cover Calabi–Yau threefold, where the model has six generations of SU(5) and the bundle is given via the spectral cover description, use a different description of the elliptic fiber which leads to more than one global section. We present two examples of a possible cover Calabi–Yau threefold with a free involution: one is a fiber product of rational elliptic surfaces dP9; another example is an elliptic fibration over a Hirzebruch surface. We compute the necessary amount of chiral matter by "turning on" a further parameter which is related to singularities of the fibration and the branching of the spectral cover.

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