scholarly journals Gap sequences of 1-Weierstrass points on non-hyperelliptic curves of genus 10

2014 ◽  
Vol 22 (3) ◽  
pp. 317-321
Author(s):  
Mohammed A. Saleem ◽  
Eslam E. Badr
Keyword(s):  
Hyperelliptic Curves ◽  
Weierstrass Points ◽  
Gap Sequences

scholarly journals Weierstrass points and gap sequences for families of curves

1994 ◽  
Vol 32 (2) ◽  
pp. 393-422 ◽  
Author(s):  
Dan Laksov ◽  
Anders Thorup
Keyword(s):  
Weierstrass Points ◽  
Families Of Curves ◽  
Gap Sequences

scholarly journals Hyperelliptic classes are rigid and extremal in genus two

2020 ◽  
Vol Volume 4 ◽  
Author(s):  
Vance Blankers
Keyword(s):  
Infinite Family ◽  
Hyperelliptic Curves ◽  
Weierstrass Points ◽  
High Codimension ◽  
Genus Two ◽  
Marked Points

We show that the class of the locus of hyperelliptic curves with $\ell$ marked Weierstrass points, $m$ marked conjugate pairs of points, and $n$ free marked points is rigid and extremal in the cone of effective codimension-($\ell + m$) classes on $\overline{\mathcal{M}}_{2,\ell+2m+n}$. This generalizes work of Chen and Tarasca and establishes an infinite family of rigid and extremal classes in arbitrarily-high codimension. Comment: Published version

scholarly journals Coleman integration for even-degree models of hyperelliptic curves

2015 ◽  
Vol 18 (1) ◽  
pp. 258-265 ◽  
Author(s):  
Jennifer S. Balakrishnan
Keyword(s):  
Number Theory ◽  
Computer Science ◽  
Hyperelliptic Curves ◽  
Open Book ◽  
Line Integral ◽  
Book Series ◽  
Numerical Examples ◽  
Lecture Notes ◽  
Integration Algorithms ◽  
Mathematical Sciences

The Coleman integral is a $p$-adic line integral that encapsulates various quantities of number theoretic interest. Building on the work of Harrison [J. Symbolic Comput. 47 (2012) no. 1, 89–101], we extend the Coleman integration algorithms in Balakrishnan et al. [Algorithmic number theory, Lecture Notes in Computer Science 6197 (Springer, 2010) 16–31] and Balakrishnan [ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Series 1 (Mathematical Sciences Publishers, 2013) 41–61] to even-degree models of hyperelliptic curves. We illustrate our methods with numerical examples computed in Sage.

scholarly journals Integral points on hyperelliptic curves

2008 ◽  
Vol 2 (8) ◽  
pp. 859-885 ◽  
Author(s):  
Yann Bugeaud ◽  
Maurice Mignotte ◽  
Samir Siksek ◽  
Michael Stoll ◽  
Szabolcs Tengely
Keyword(s):  
Hyperelliptic Curves ◽  
Integral Points
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