论文标题
曲线相对伯格曼内核度量的边界渐近学
Boundary asymptotics of the relative Bergman kernel metric for curves
论文作者
论文摘要
我们研究了伯格曼核心核心对变性的卑鄙的riemann表面及其雅各比式品种的相对伯格曼内核指标的行为。在节点或尖端附近，我们获得具有明确系数的精确渐近公式。通常，给定的cuspidal家族上的伯格曼内核并不总是会在极限表面的常规部分汇聚，这与淋巴结案不同。事实证明，有关奇异性和复杂结构的信息都促进了伯格曼内核的各种渐近行为。我们的方法涉及阿贝尔差异和周期矩阵的经典泰勒扩展。
We study the behaviors of the relative Bergman kernel metrics on holomorphic families of degenerating hyperelliptic Riemann surfaces and their Jacobian varieties. Near a node or cusp, we obtain precise asymptotic formulas with explicit coefficients. In general the Bergman kernels on a given cuspidal family do not always converge to that on the regular part of the limiting surface, which is different from the nodal case. It turns out that information on both the singularity and complex structure contributes to various asymptotic behaviors of the Bergman kernel. Our method involves the classical Taylor expansion for Abelian differentials and period matrices.
