Focal loci of families and the genus of curves on surfaces

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dc.creatorChiantini, L.
dc.creatorLopez, A. F.
dc.date1999-03-08
dc.date2001-04-23
dc.date.accessioned2026-07-07T05:28:15Z
dc.date.available2026-07-07T05:28:15Z
dc.descriptionIn this article we apply the classical method of focal loci of families to give a lower bound for the genus of curves lying on general surfaces. First we translate and reprove Xu's result that any curve C on a general surface in P^3 of degree d>4 has geometric genus g > 1 + deg(C)(d - 5)/2. Then we prove a similar lower bound for the curves lying on a general surface in a given component of the Noether-Lefschetz locus in P^3 and on a general projectively Cohen-Macaulay surface in P^4.
dc.descriptionPlain TeX, 11 pages, to appear on PAMS. Minor corrections in the statement of 1.3 and in remark 3.4
dc.identifierhttps://arxiv.org/abs/math/9903044
dc.identifierhttp://arxiv.org/abs/math/9903044
dc.identifierPAMS n. 127/12
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78190
dc.subjectAlgebraic Geometry
dc.subject14J29
dc.titleFocal loci of families and the genus of curves on surfaces
dc.typetext

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