Conic bundles that are not birational to numerical Calabi-Yau pairs. (Fibrés en coniques qui ne sont pas birationnels à des paires de Calabi-Yau numériques.) (English. French summary) Zbl 1494.14053
Summary: Let \(X\) be a general conic bundle over the projective plane with branch curve of degree at least 19. We prove that there is no normal projective variety \(Y\) that is birational to \(X\) and such that some multiple of its anticanonical divisor is effective. We also give such examples for 2-dimensional conic bundles defined over a number field.
MSC:
14M22 | Rationally connected varieties |
14J45 | Fano varieties |
14J20 | Arithmetic ground fields for surfaces or higher-dimensional varieties |
14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
14E05 | Rational and birational maps |