## Kollár, János - Conic bundles that are not birational to numerical Calabi--Yau pairs

epiga:1518 - Épijournal de Géométrie Algébrique, September 1, 2017, Volume 1
Conic bundles that are not birational to numerical Calabi--Yau pairs

Authors: Kollár, János

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.

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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