论文标题
短纤维双曲线表面的短同源碱基
Short homology bases for hyperelliptic hyperbolic surfaces
论文作者
论文摘要
鉴于过度椭圆表面$ s $ s $属$ g \ geq 2 $，我们在$ s $上找到了同源独立环的长度。结果，我们表明，对于任何$λ\（0,1）$中的任何$λ\都存在一个常数$ n（λ）$，因此每个这样的表面至少具有$ \lceilλ\ cdot \ cdot \ cdot \ frac {2} {3} g \ rceil $ fromicalical $ fromicalical $ fromical $ fromical $ nepptionallicalicalical $ bps $ n（λ）$的长度独立循环这使我们能够在[MU]中扩展在[MU]中获得的恒定上限，这是在非零周期晶格载体的最小长度上，即几乎是$ \ frac {2} {3} g $线性独立的矢量。
Given a hyperelliptic hyperbolic surface $S$ of genus $g \geq 2$, we find bounds on the lengths of homologically independent loops on $S$. As a consequence, we show that for any $λ\in (0,1)$ there exists a constant $N(λ)$ such that every such surface has at least $\lceil λ\cdot \frac{2}{3} g \rceil$ homologically independent loops of length at most $N(λ)$, extending the result in [Mu] and [BPS]. This allows us to extend the constant upper bound obtained in [Mu] on the minimal length of non-zero period lattice vectors of hyperelliptic Riemann surfaces to almost $\frac{2}{3} g$ linearly independent vectors.
