1997/03/07 by Ciro Ciliberto, C. Ciliberto, Klaus Hulek +3
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Mathematics and Applications #Point processes and geometric inequalities #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9703009
LaTeX2e with theorem, amstex, amssymb, amscd packages; 11 pages
arxiv created 1997/03/07 · openalex publication_date 1997/03/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The union of two quintic elliptic scrolls in P4 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 P4, 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 P4. Here we consider the analogous situation in higher dimensional projective spaces Pn-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.