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摘要翻译：
设K是不同于2的特征域，C是由Weierstrass方程给出的K上的椭圆曲线。要把C族的一个元素除以2，就必须解一个四次方程。我们刻画了由这个过程产生的四次数，并找出四次数决定曲线和点的程度。我们找到了由2-和3-扭转点的2-除法得到的四次型，并将这种对应关系推广到奇异平面三次型。利用这些结果，我们研究了哪些4次曲线映射可以实现为椭圆曲面上多截面的复制。
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英文标题：
《Quartic equations and 2-division on elliptic curves》
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作者：
George H. Hitching
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let K be a field of characteristic different from 2 and C an elliptic curve over K given by a Weierstrass equation. To divide an element of the group C by 2, one must solve a certain quartic equation. We characterise the quartics arising from this procedure and find how far the quartic determines the curve and the point. We find the quartics coming from 2-division of 2- and 3-torsion points, and generalise this correspondence to singular plane cubics. We use these results to study the question of which degree 4 maps of curves can be realised as duplication of a multisection on an elliptic surface.
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PDF链接：
https://arxiv.org/pdf/0706.4379
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