标题： 通过分支覆盖的扰动分裂代数奇点纤维化 显示英文标题

标题： Splitting Algebraic Singular Fibrations via Perturbation of Branch Covers

摘要： 在先前的论文\cite{SV}中，作者研究了在某些二元纤维的代数纤维化中可能出现的孤立奇点纤维。 在那里，目标是确定它们的单色因子分解，以确定一组曲线配置与映射类群中某些单词之间的字典。 每种这样的曲线配置最初由 Namikawa 和 Ueno\cite{NamikawaUeno-list}在他们关于二元纤维的列表中进行分类。 我们研究了四类多项式，我们限制在纤维具有边界的纤维化中，考虑了引用在\cite{NamikawaUeno-list}中的孤立仿射奇点。 我们消解了奇点，并使用经过仔细选择的扰动，将它们变形为 Lefschetz 纤维化并确定了它们的单色因子分解。 在其中两类中，我们也获得了关于中心纤维在闭合纤维纤维化中紧化方式的强信息。 在本文中，我们通过使用另一类多项式来重新创建奇点纤维，处理其余两种情况。 在\cite{SV}中，所有纤维中的代数曲线都被明确地表示为双曲方程。 我们利用这种对称性来构造变形并恢复单色因子分解。 在本文中，曲线不再被明确地表示为双曲的——商曲线不再只是$\CC$，分支曲线也不再嵌入在$\CC^2$中，并且在商中使用的纤维现在更加复杂。 不过，我们确实恢复了中心纤维紧化所需的性质、其变形为 Lefschetz 纤维化以及相应的单色因子分解。 显示英文摘要

摘要： In a previous paper \cite{SV}, the authors studied the isolated singular fibers that can occur in algebraic fibrations of certain genus two fibrations. There the goal was to determine their monodromy factorizations with the goal of determining a dictionary between a set of curve configurations and certain words in the mapping class group. Each such curve configuration was originally cataloged by Namikawa and Ueno \cite{NamikawaUeno-list} in their list of genus two fibrations. We studied four families of polynomials, we restricted to fibrations whose fibers have boundary, considering the isolated affine singularity referenced in \cite{NamikawaUeno-list}. We resolved the singularities and, using carefully chosen perturbations, deformed them into Lefschetz fibrations and determined their monodromy factorizations. In two of those families, we also obtained strong information about how the central fiber compactifies in a fibration with closed fibers. In this paper we work on the other two cases by recreating the singular fibers using a different family of polynomials. In \cite{SV}, all the algebraic curves in the fibrations were given expressly as hyperelliptic equations. We utilized this symmetry both to construct the deformation and to recover the monodromy factorization. In this paper the curves are no longer expressly hyperelliptic--the quotient curve is no longer just $\CC$, the branch curves are no longer embedded in $\CC^2$, and the fibrations utilized in the quotient are now more complicated. We do, though, recover the desired behavior of the compactification of the central fiber, its deformation to a Lefschetz fibration, and the corresponding monodromy factorization.