On Surfaces of General Type
نویسنده
چکیده
We study nonsingular minimal surfaces of general type with pg = 6 and K2 = 13 whose canonical image is contained in a single nonsingular quadric. We show that under these assumptions, such surfaces are regular and their canonical ideal has codimension 3. Led by Buchsbaum–Eisenbud’s structure theorem, we define a map of S into a weighted Grassmannian, which factors through an embedding of the canonical model of S. We achieve this by constructing a bundle on S with appropriate invariants. We deduce that the canonical model of S is a complete intersection of four quasihomogeneous forms of degree 2 in a weighted Grassmannian.
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