Injectivity radius and gonality of a compact Riemann surface
Injectivity radius and gonality of a compact Riemann surface
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紧致黎曼曲面的注入半径和正交性
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
W. To
中科院分区：
文献类型：
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作者：
Jun;W. To
在紧致黎曼曲面与自身的笛卡尔积对角线的测地线管状邻域中，我们得到了纯$1$维复解析子变量体积的一个明显下界。这导致了笛卡尔积相对于对角线的规范线束的Seshadri数的下界。由此，我们得到了固定向性的紧黎曼曲面的双曲注入半径的上界。特别地，我们得到了紧黎曼曲面塔的泛性的极限行为。我们还将所得结果应用于与黎曼曲面对称积的样锥有关的不变量。
We obtain a sharp lower bound for the volumes of purely $1$-dimensional complex analytic subvarieties in a geodesic tubular neighborhood of the diagonal of the Cartesian product of a compact Riemann surface with itself. This leads to a lower bound of the Seshadri number of the canonical line bundle of the Cartesian product with respect to the diagonal. As a consequence, we obtain an upper bound for the hyperbolic injectivity radii of compact Riemann surfaces of a fixed gonality. In particular, we obtain the limiting behavior of the gonalities of a tower of compact Riemann surfaces. We also give an application of our results to an invariant related to the ample cone of the symmetric product of a Riemann surface.