A Remark on the Geometry of Elliptic Scrolls and Bielliptic Surfaces

dc.creatorCiliberto, C.
dc.creatorHulek, K.
dc.date1997-03-07
dc.date.accessioned2026-07-07T09:07:12Z
dc.date.available2026-07-07T09:07:12Z
dc.descriptionThe union of two quintic elliptic scrolls in P^4 intersecting transversally along an elliptic normal quintic curve is a singular surface Z which behaves numerically like a bielliptic surface. In the appendix to the paper [W. Decker et al.: Syzygies of abelian and bielliptic surfaces in P^4, alg-geom/9606013] where the equations of this singular surface were computed, we proved that Z defines a smooth point in the appropriate Hilbert scheme and that Z cannot be smoothed in P^4. Here we consider the analogous situation in higher dimensional projective spaces P^{n-1}, where, to our surprise, the answer depends on the dimension n-1. If n is odd the union of two scrolls cannot be smoothed, whereas it can be smoothed if n is even. We construct an explicit smoothing.
dc.descriptionLaTeX2e with theorem, amstex, amssymb, amscd packages; 11 pages
dc.identifierhttps://arxiv.org/abs/alg-geom/9703009
dc.identifierhttp://arxiv.org/abs/alg-geom/9703009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150284
dc.subjectAlgebraic Geometry
dc.titleA Remark on the Geometry of Elliptic Scrolls and Bielliptic Surfaces
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