Surface of Class VII
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, surfaces of class VII are non-algebraic complex surfaces studied by (Kodaira 1964, 1968) that have Kodaira dimension and first Betti number 1. Minimal surfaces of class VII (those with no rational curves with self-intersection 1) are called surfaces of class VII0. Every class VII surface is birational to a unique minimal class VII surface, and can be obtained from this minimal surface by blowing up points a finite number of times. The name "class VII" ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, surfaces of class VII are non-algebraic complex surfaces studied by (Kodaira 1964, 1968) that have Kodaira dimension and first Betti number 1. Minimal surfaces of class VII (those with no rational curves with self-intersection 1) are called surfaces of class VII0. Every class VII surface is birational to a unique minimal class VII surface, and can be obtained from this minimal surface by blowing up points a finite number of times. The name "class VII" comes from (Kodaira 1964, theorem 21), which divided minimal surfaces into 7 classes numbered I0 to VII0. However Kodaira''s class VII0 did not have the condition that the Kodaira dimension is , but instead had the condition that the geometric genus is 0. As a result, his class VII0 also included some other surfaces, such as secondary Kodaira surfaces, that are no longer considered to be class VII as they do not have Kodaira dimension . The minimal surfaces of class VII are the class numbered "7" on the list of surfaces in (Kodaira 1968, theorem 55).
