The irreducibility of certain pure-cycle Hurwitz spaces

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dc.creatorLiu, Fu
dc.creatorOsserman, Brian
dc.date2006-09-04
dc.date.accessioned2026-07-07T07:24:30Z
dc.date.available2026-07-07T07:24:30Z
dc.descriptionWe study "pure-cycle" Hurwitz spaces, parametrizing covers of the projective line having only one ramified point over each branch point. We start with the case of genus-0 covers, using a combination of limit linear series theory and group theory to show that these spaces are always irreducible. In the case of four branch points, we also compute the associated Hurwitz numbers. Finally, we give a conditional result in the higher-genus case, requiring at least 3g simply branched points. These results have equivalent formulations in group theory, and in this setting complement results of Conway-Fried-Parker-Volklein.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0609118
dc.identifierhttp://arxiv.org/abs/math/0609118
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116378
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subject14H10; 05A15
dc.titleThe irreducibility of certain pure-cycle Hurwitz spaces
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