Transversality of sections on elliptic surfaces with applications to elliptic divisibility sequences and geography of surfaces

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dc.contributor.authorUlmer, Douglas
dc.contributor.authorUrzua, Giancarlo
dc.date.accessioned2025-01-20T22:01:18Z
dc.date.available2025-01-20T22:01:18Z
dc.date.issued2022
dc.description.abstractWe consider elliptic surfaces epsilon over a field k equipped with zero section O and another section P of infinite order. If k has characteristic zero, we show there are only finitely many points where O is tangent to a multiple of P. Equivalently, there is a finite list of integers such that if n is not divisible by any of them, then nP is not tangent to O. Such tangencies can be interpreted as unlikely intersections. If k has characteristic zero or p > 3 and epsilon is very general, then we show there are no tangencies between O and nP. We apply these results to square-freeness of elliptic divisibility sequences and to geography of surfaces. In particular, we construct mildly singular surfaces of arbitrary fixed geometric genus with K ample and K-2 unbounded.
dc.fuente.origenWOS
dc.identifier.doi10.1007/s00029-021-00747-x
dc.identifier.eissn1420-9020
dc.identifier.issn1022-1824
dc.identifier.urihttps://doi.org/10.1007/s00029-021-00747-x
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/93808
dc.identifier.wosidWOS:000736590000008
dc.issue.numero2
dc.language.isoen
dc.revistaSelecta mathematica-new series
dc.rightsacceso restringido
dc.subjectElliptic surfaces
dc.subjectUnlikely intersections
dc.subjectElliptic divisibility sequences
dc.subjectStable surfaces
dc.subjectGeography of surfaces
dc.titleTransversality of sections on elliptic surfaces with applications to elliptic divisibility sequences and geography of surfaces
dc.typeartículo
dc.volumen28
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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