论文标题
血ellip曲线的单肌问题
The Monodromy problem for hyperelliptic curves
论文作者
论文摘要
我们研究了与多项式直接总和的单构图相关的Dynkin图。单肌问题询问在多项式的哪些条件下，消失的周期的单片产生了常规纤维的整个同源性。我们考虑了$ y^4+g（x）$的情况，这是Christopher和Marde $ \ check {s} $Ić的结果的概括。此外，我们解决了第四级多项式的直接总和的单肌问题。
We study the Dynkin diagram associated to the monodromy of direct sums of polynomials. The monodromy problem asks under which conditions on a polynomial, the monodromy of a vanishing cycle generates the whole homology of a regular fiber. We consider the case $y^4+g(x)$, which is a generalization of the results of Christopher and Marde$\check{s}$ić about the monodromy problem for hyperelliptic curves. Moreover, We solve the monodromy problem for direct sums of fourth degree polynomials.
