Geodesic
Conic bundles that are not birational to numerical Calabi–Yau pairs
Épijournal de Géométrie Algébrique, Tome 1 (2017)

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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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     author = {Koll\'ar, J\'anos},
     title = {Conic bundles that are not birational to numerical {Calabi{\textendash}Yau} pairs},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     year = {2017},
     doi = {10.46298/epiga.2017.volume1.1518},
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Kollár, János. Conic bundles that are not birational to numerical Calabi–Yau pairs. Épijournal de Géométrie Algébrique, Tome 1 (2017). doi: 10.46298/epiga.2017.volume1.1518

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