Algebraic surfaces

Algebraic surfaces

The previous result shows that a minimal model for surface always exists and that a surface X is minimal if and only if X has no (−1)curve. Hence we may and we usually do assume that X is minimal. However, the criterion by (−1) curve only valid for surface. We might prefer to have a criterion which is also valid for higher dimension. If X has a (−1)-curve E, then KX .E = −1 < 0. Thus if KX is n...

ALGEBRAIC SURFACES WITH ' q

Open Algebraic Surfaces

To put the subject matter of " Open Algebraic Surfaces " in perspective, let me begin with a very classical question: If k ⊂ L are fields and L ⊂ k(x 1 , · · · , x n) = k (n) (field of rational functions), is L purely transcendental over k? (Then L = k (d) , d = transcendence degree of L over k. This is the " right " measure for the dimension of the problem, one can easily reduce it to the case...

Complex Algebraic Surfaces Class 16

Complex Algebraic Surfaces Class 17