发表机构
University of Minnesota; Purdue University（明尼苏达大学; 普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究 Cartwright-Steger 曲面的亏格-19 Albanese 纤维化，通过轨道商建立单值关系，并利用双典范束构造次数为 72 的映射，生成纤维同调。
AI 中文摘要
我们研究 Cartwright–Steger 曲面的亏格-19 Albanese 纤维化及其三阶对称性。通过取椭圆基的轨道折叠商，我们得到了两个柄单值算子与三个关于消失环的 Dehn 扭转之间的关系。两条实消失路径给出了实不动点位于不变纤维的不同椭圆上的环。对于循环三重覆盖，我们将一条曲线与其在覆盖变换下的像的交点表示为商上的带符号交叉数。我们确定了次数为 72 的双典范束在节点附近的两个局部分支值，并研究了一个对称的双典范束。一个一般的束还给出了从曲面的 blowup 到椭圆曲线与射影直线之积的有限次数为 72 的映射。节点消失类的单值平移生成光滑纤维的第一同调群。
英文摘要
We study the genus-$19$ Albanese fibration of the Cartwright--Steger surface and its order-three symmetry. Passing to the orbifold quotient of the elliptic base gives a relation among the two handle monodromies and the three Dehn twists about the vanishing cycles. The two real vanishing paths give cycles whose real fixed points lie on different ovals of the invariant fiber. For a cyclic triple cover, we express the intersection of a curve with its image under the deck transformation as a signed crossing count on the quotient. We determine the two local branch values of a degree-$72$ bicanonical pencil near a node and study a symmetric bicanonical pencil. A general pencil also gives a finite degree-$72$ map from a blowup of the surface to the product of the elliptic curve and a projective line. The monodromy translates of the nodal vanishing classes span the first homology of a smooth fiber.
Comments11 pages
