scholarly journals Distinguishing elliptic fibrations with AI

2019 ◽  
Vol 798 ◽  
pp. 134889 ◽  
Author(s):  
Yang-Hui He ◽  
Seung-Joo Lee
Keyword(s):  
Elliptic Fibrations

scholarly journals Elliptic Fibrations and Kodaira Dimensions of Schreieder’s Varieties

2021 ◽  
Author(s):  
Alice Garbagnati
Keyword(s):  
K3 Surfaces ◽  
Base Change ◽  
Kodaira Dimension ◽  
Elliptic Surface ◽  
Minimal Resolution ◽  
Elliptic Fibrations ◽  
Smooth Model ◽  
Birational Model ◽  
Hodge Numbers ◽  
Rational Elliptic Surface

Abstract We discuss the birational geometry and the Kodaira dimension of certain varieties previously constructed by Schreieder, proving that in any dimension they admit an elliptic fibration and they are not of general type. The $l$-dimensional variety $Y_{(n)}^{(l)}$, which is the quotient of the product of a certain curve $C_{(n)}$ by itself $l$ times by a group $G\simeq \left ({\mathbb{Z}}/n{\mathbb{Z}}\right )^{l-1}$ of automorphisms, was constructed by Schreieder to obtain varieties with prescribed Hodge numbers. If $n=3^c$ Schreieder constructed an explicit smooth birational model of it, and Flapan proved that the Kodaira dimension of this smooth model is 1, if $c>1$; if $l=2$ it is a modular elliptic surface; if $l=3$ it admits a fibration in K3 surfaces. In this paper we generalize these results: without any assumption on $n$ and $l$ we prove that $Y_{(n)}^{(l)}$ admits many elliptic fibrations and its Kodaira dimension is at most 1. Moreover, if $l=2$, its minimal resolution is a modular elliptic surface, obtained by a base change of order $n$ on a specific extremal rational elliptic surface; if $l\geq 3$ it has a birational model that admits a fibration in K3 surfaces and a fibration in $(l-1)$-dimensional varieties of Kodaira dimension at most 0.

scholarly journals On the equidistribution of some Hodge loci

2020 ◽  
Vol 2020 (762) ◽  
pp. 167-194
Author(s):  
Salim Tayou
Keyword(s):  
Hodge Structure ◽  
K3 Surfaces ◽  
Elliptic Fibrations ◽  
Projective Curves ◽  
Variations Of Hodge Structure

AbstractWe prove the equidistribution of the Hodge locus for certain non-isotrivial, polarized variations of Hodge structure of weight 2 with {h^{2,0}=1} over complex, quasi-projective curves. Given some norm condition, we also give an asymptotic on the growth of the Hodge locus. In particular, this implies the equidistribution of elliptic fibrations in quasi-polarized, non-isotrivial families of K3 surfaces.

scholarly journals Classifications of Elliptic Fibrations of a Singular K3 Surface

2015 ◽  
pp. 17-49 ◽  
Author(s):  
Marie José Bertin ◽  
Alice Garbagnati ◽  
Ruthi Hortsch ◽  
Odile Lecacheux ◽  
Makiko Mase ◽  
...  
Keyword(s):  
K3 Surface ◽  
Elliptic Fibrations

Mini-Workshop: Higher Dimensional Elliptic Fibrations

2010 ◽  
pp. 2651-2680
Author(s):  
Gavin Brown ◽  
Anda Degeratu ◽  
Katrin Wendland
Keyword(s):  
Elliptic Fibrations ◽  
Higher Dimensional

DENSITY OF POSITIVE RANK FIBERS IN ELLIPTIC FIBRATIONS, II

2010 ◽  
Vol 06 (01) ◽  
pp. 15-23 ◽  
Author(s):  
RITABRATA MUNSHI
Keyword(s):  
Real Number ◽  
Number Field ◽  
Elliptic Fibrations ◽  
Dense Set ◽  
Positive Rank ◽  
Real Number Field

We show that for a quartic elliptic fibration over a real number field, existence of two positive rank fibers implies existence of a dense set of positive rank fibers. We also prove the same result for certain sextic families.

scholarly journals Linear Growth for Certain Elliptic Fibrations

2015 ◽  
Vol 2015 (21) ◽  
pp. 10859-10871 ◽  
Author(s):  
Pierre Le Boudec
Keyword(s):  
Linear Growth ◽  
Elliptic Fibrations

scholarly journals Stable sheaves on elliptic fibrations

2002 ◽  
Vol 43 (2-3) ◽  
pp. 163-183 ◽  
Author(s):  
D.Hernández Ruipérez ◽  
J.M. Muñoz Porras
Keyword(s):  
Elliptic Fibrations ◽  
Stable Sheaves

scholarly journals ON ELEVATING FREE-FERMION Z2×Z2 ORBIFOLDS MODELS TO COMPACTIFICATIONS OF F THEORY

2000 ◽  
Vol 15 (09) ◽  
pp. 1345-1362 ◽  
Author(s):  
P. BERGLUND ◽  
J. ELLIS ◽  
A. E. FARAGGI ◽  
D. V. NANOPOULOS ◽  
Z. QIU
Keyword(s):  
Singular Points ◽  
Free Fermion ◽  
Gravitational Anomaly ◽  
Elliptic Fibrations ◽  
Common Framework ◽  
The Common ◽  
Six Dimensions

We study the elliptic fibrations of some Calabi–Yau threefolds, including the Z2×Z2 orbifold with (h1,1,h2,1)=(27, 3), which is equivalent to the common framework of realistic free-fermion models, as well as related orbifold models with (h1,1,h2,1)=(51, 3) and (31, 7). However, two related puzzles arise when one considers the (h1,1,h2,1)=(27, 3) model as an F theory compactification to six dimensions. The condition for the vanishing of the gravitational anomaly is not satisfied, suggesting that the F theory compactification does not make sense, and the elliptic fibration is well defined everywhere except at four singular points in the base. We speculate on the possible existence of N=1 tensor and hypermultiplets at these points which would cancel the gravitational anomaly in this case.

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