Journals / Turkish Journal of Mathematics / 2005 / Cilt: 29 - Sayı: 2
Constructing New K3 Surfaces
- Pages
- 175–192
- DOI
- —
Abstract
This paper is concerned with a method based on birational geometry and produces dozens of new examples in codimensions 3, 4, 5 etc. The method is called unprojection by Reid. Using this method we construct new examples of K3 surfaces of codimensions 3 and 4 in weighted projective spaces from smaller codimension K3 surfaces whose rings are much simpler. This leads to the existence of almost all candidates for codimension 3 K3 surfaces in the list.
Özet
This paper is concerned with a method based on birational geometry and produces dozens of new examples in codimensions 3, 4, 5 etc. The method is called unprojection by Reid. Using this method we construct new examples of K3 surfaces of codimensions 3 and 4 in weighted projective spaces from smaller codimension K3 surfaces whose rings are much simpler. This leads to the existence of almost all candidates for codimension 3 K3 surfaces in the list.