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arXiv · 1605.04763

Conic bundles that are not birational to numerical Calabi--Yau pairs

János Kollár
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Abstract

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.

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János Kollár. 2016-05-16. Conic bundles that are not birational to numerical Calabi--Yau pairs. https://doi.org/10.46298/epiga.2017.volume1.1518

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