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.

Source : oai:arXiv.org:1605.04763

Volume: Volume 1

Published on: September 1, 2017

Submitted on: March 14, 2017

Keywords: Mathematics - Algebraic Geometry,14M22, 14J45, 14J20 (Primary), 14J32, 14E05 (Secondary)

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