Cubic forms, powers of primes and classification of elliptic curves

2021 ◽  
Author(s):  
Karolina Chałupka
Keyword(s):  
Elliptic Curves ◽  
Cubic Forms

scholarly journals On the singularity structure of Kahan discretizations of a class of quadratic vector fields

2021 ◽  
Author(s):  
René Zander
Keyword(s):  
Elliptic Curves ◽  
Vector Fields ◽  
Singularity Structure ◽  
Quadratic Vector Fields ◽  
Parameter Values

AbstractWe discuss the singularity structure of Kahan discretizations of a class of quadratic vector fields and provide a classification of the parameter values such that the corresponding Kahan map is integrable, in particular, admits an invariant pencil of elliptic curves.

scholarly journals Classification of cubic forms with three variables

1981 ◽  
Vol 10 (2) ◽  
pp. 239-248
Author(s):  
Tadayuki ABIKO
Keyword(s):  
Cubic Forms

Derived Category and Canonical Bundle – I

2007 ◽  
Author(s):  
D. Huybrechts
Keyword(s):  
Elliptic Curves ◽  
Derived Categories ◽  
Derived Category ◽  
Canonical Bundle ◽  
Smooth Curves ◽  
Coherent Sheaves

This chapter is devoted to results by Bondal and Orlov which show that for varieties with ample (anti-)canonical bundle, the bounded derived category of coherent sheaves determines the variety. Except for the case of elliptic curves, this settles completely the classification of derived categories of smooth curves. The complexity of the derived category is reflected by its group of autoequivalences. This is studied by means of ample sequences.

scholarly journals Minimal models for -coverings of elliptic curves

2014 ◽  
Vol 17 (A) ◽  
pp. 112-127
Author(s):  
Tom Fisher
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Minimal Model ◽  
Rational Points ◽  
Minimal Models ◽  
Integer Coefficients ◽  
Field Extensions ◽  
Cubic Forms ◽  
New Formula

AbstractIn this paper we give a new formula for adding $2$-coverings and $3$-coverings of elliptic curves that avoids the need for any field extensions. We show that the $6$-coverings obtained can be represented by pairs of cubic forms. We then prove a theorem on the existence of such models with integer coefficients and the same discriminant as a minimal model for the Jacobian elliptic curve. This work has applications to finding rational points of large height on elliptic curves.

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