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

epiga:1518 - Épijournal de Géométrie Algébrique, September 1, 2017, Volume 1 - https://doi.org/10.46298/epiga.2017.volume1.1518
Conic bundles that are not birational to numerical Calabi--Yau pairs

Authors: János Kollár

    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
    Accepted on: March 14, 2017
    Submitted on: March 14, 2017
    Keywords: Mathematics - Algebraic Geometry,14M22, 14J45, 14J20 (Primary), 14J32, 14E05 (Secondary)
    Fundings :
      Source : OpenAIRE Research Graph
    • Families of varieties of general type; Funder: National Science Foundation; Code: 1362960

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