scholarly journals Hyperelliptic Jacobians as billiard algebra of pencils of quadrics: Beyond Poncelet porisms

2008 ◽  
Vol 219 (5) ◽  
pp. 1577-1607 ◽  
Author(s):  
Vladimir Dragović ◽  
Milena Radnović
Keyword(s):  
Pencils Of Quadrics ◽  
Hyperelliptic Jacobians

scholarly journals The Veronesean of quadrics and associated loci

1936 ◽  
Vol 5 (1) ◽  
pp. 14-25
Author(s):  
J. W. Head
Keyword(s):  
Three Dimensions ◽  
Cubic Surface ◽  
Polar System ◽  
Twisted Cubic ◽  
Pencils Of Quadrics

In this paper we consider the correspondence between tangential quadrics of [3] and points of [9]. Godeaux has considered this geometrically, with the object of obtaining a representation for a twisted cubic of three dimensions. We have considered it from a standpoint more algebraic than that of Godeaux, with particular reference to the types of pencils of quadrics that correspond to special lines of [9], and to the interpretation in [9] of the fact that the condition for a net of quadrics to be part of the polar system of a cubic surface is poristic.

scholarly journals Canonical heights and division polynomials

2014 ◽  
Vol 157 (2) ◽  
pp. 357-373 ◽  
Author(s):  
ROBIN de JONG ◽  
J. STEFFEN MÜLLER
Keyword(s):  
Recurrence Relation ◽  
Number Field ◽  
Diophantine Approximation ◽  
New Method ◽  
Approximation Result ◽  
Algebraic Point ◽  
Canonical Height ◽  
Division Polynomials ◽  
Genus 2 ◽  
Hyperelliptic Jacobians

AbstractWe discuss a new method to compute the canonical height of an algebraic point on a hyperelliptic jacobian over a number field. The method does not require any geometrical models, neitherp-adic nor complex analytic ones. In the case of genus 2 we also present a version that requires no factorisation at all. The method is based on a recurrence relation for the ‘division polynomials’ associated to hyperelliptic jacobians, and a diophantine approximation result due to Faltings.

Sign in / Sign up

Export Citation Format

Share Document