机构:
Oakland Univ, Rochester, MI 48063 USAOakland Univ, Rochester, MI 48063 USA
Shaska, T.
[1
]
Beshaj, L.
论文数: 0引用数: 0
h-index: 0
机构:
Oakland Univ, Rochester, MI 48063 USA
Princeton Univ, Dept Math, Princeton, NJ 08544 USAOakland Univ, Rochester, MI 48063 USA
Beshaj, L.
[1
,2
]
机构:
[1] Oakland Univ, Rochester, MI 48063 USA
[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
来源:
ADVANCES ON SUPERELLIPTIC CURVES AND THEIR APPLICATIONS
|
2015年
/
41卷
关键词:
algebraic curves;
heights;
moduli height;
D O I:
10.3233/978-1-61499-520-3-137
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
In these lectures we cover basics of the theory of heights starting with the heights in the projective space, heights of polynomials, and heights of the algebraic curves. We define the minimal height of binary forms and moduli height for algebraic curves and prove that the moduli height of superelliptic curves H(f) <= c(0)(H) over tilde (f) where c(0) is a constant and (H) over tilde the minimal height of the corresponding binary form. For genus g = 2 and 3 such constant is explicitly determined. Furthermore, complete lists of curves of genus 2 and genus 3 hyperelliptic curves with height 1 are computed.
机构:
Natl Res Univ Higher Sch Econ, Moscow, Russia
Russian Acad Sci SRISA, Fed State Inst, Sci Res Inst Syst Anal, Moscow, RussiaNatl Res Univ Higher Sch Econ, Moscow, Russia