Twistors, Quartics, and del Pezzo Fibrations

We investigate the structure of a variety new Moishezon twistor spaces, by utilizing pluri-half-anti-canonical map from spaces. Each these spaces is bimeromorphic to double covering scroll planes over rational normal curve, and branch divisor cover cut quartic hypersurface. In particular, has pencil Del Pezzo surfaces degree two. Correspondingly, have with big anti-canonical class. The base locus last cycle curves, it an curve on smooth members pencil. These are naturally classified into four types according type singularities divisor, or equivalently, those in also show that hypersurface satisfies strong constraint as result defining polynomial be specific form. Together our previous result, present completes classification whose half-anti-canonical system Twistor larger than been understood for long time before. opposite direction, no example known space smaller