or less on the "Noether line" edge of the region of possible values of the Chern numbers). They are all simply connected, and Horikawa gave a detailed description of them. Products: the product of two curves both of genus at least 2 is a surface of general type. Double covers of non-singular degree 2m curves in P2 are of general type if (For 2m=2 they are rational, for 2m=4 they are again rational and called del Pezzo double planes, and for 2m=6 they are K3 surfaces.) They are simply connected, and have Chern numbers Canonical models proved that the multicanonical map φnK for a complex surface of general type is a birational isomorphism onto its image whenever n≥5, and showed that the same result still holds in positive characteristic. There are some surfaces for which it is not a birational isomorphism when n is 4. These results follow from Reider's theorem. See also Enriques–Kodaira classification List of algebraic surfaces Notes References Algebraic surfaces Birational geometry Complex surfaces