A Little Algebraic Surface Theory
Let us return to geometry armed with what we have learned so far. We have already looked at Riemann surfaces (which will be referred to as complex curves from now on) in some detail. So we consider the next step up. A nonsingular complex surface is a two-dimensional complex manifold. By an algebraic surface, we will mean a two-dimensional nonsingular projective variety. So in particular, they are Kähler manifolds. In this chapter, we will present a somewhat breezy account of surface theory, concentrating on topics that illustrate the general theorems from the previous chapters.
KeywordsAlgebraic Surface Elliptic Surface Hodge Number Canonical Divisor Smooth Projective Curve
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