2002/09/23 by Ciro Ciliberto, Rick Miranda, Mina Teicher
Mathematics · #math.AG #msc:14J28
published as In: "Applications of Algebraic Geometry to Coding Theory, Physics, and Computation", NATO Science Series II, Vol. 36 (2001), 53-64 · 10 pages
arxiv created 2002/09/23 · arxiv updated 2009/11/30
In this article we construct a specific projective degeneration of K3 surfaces of degree 2g-2 in Pg to a union of 2g-2 planes, which meet in such a way that the combinatorics of the configuration of planes is a triangulation of the 2-sphere. Abstractly, such degenerations are said to be Type III degenerations of K3 surfaces. Although the birational geometry of such degenerations is fairly well understood, the study of projective degenerations is not nearly as completely developed. In this article we construct degenerations for which the general member is embedded by a multiple of the primitive line bundle class.