On the Slope of Hyperelliptic Lefschetz Fibrations and the Number of Separating Vanishing Cycles

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dc.creatorGurtas, Yusuf Z
dc.date2008-10-07
dc.date2008-10-23
dc.date.accessioned2026-07-07T10:12:19Z
dc.date.available2026-07-07T10:12:19Z
dc.descriptionIn this article we find an upper and lower bound for the slope of genus g hyperelliptic Lefschetz fibrations, which is sharp when g = 2, and demonstrate the strong connection, in general, between the slope of hyperelliptic genus g Lefschetz fibrations and the number of separating vanishing cycles. Specifically, we show that the slope is greater than 4-4/g if and only if the fibration contains separating vanishing cycles. We also improve the existing bound on s/n, the ratio of number of separating vanishing cycles to the number of non-separating vanishing cycles, for hyperelliptic Lefschetz fibrations of genus g>1. In particular we show that s<=n for such fibrations when g>5.
dc.description23 Pages, Corollary 19 and Corollary 23 added
dc.identifierhttps://arxiv.org/abs/0810.1088
dc.identifierhttp://arxiv.org/abs/0810.1088
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172145
dc.subjectSymplectic Geometry
dc.subjectGeometric Topology
dc.subject57R17, 14J99
dc.titleOn the Slope of Hyperelliptic Lefschetz Fibrations and the Number of Separating Vanishing Cycles
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