Rational curves and strictly nef divisors on Calabi-Yau threefolds

  • Haidong Liu

    Sun Yat-sen University, Department of Mathematics, Guangzhou, 510275, China
  • Roberto Svaldi

    École Polytechnique Fédérale de Lausanne, EPFL SB MATH (Bâtiment MA), Station 8, CH-1015 Lausanne, Switzerland
Rational curves and strictly nef divisors on Calabi-Yau threefolds cover
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Abstract

We give a criterion for a nef divisor to be semi-ample on a Calabi-Yau threefold when and . As a direct consequence, we show that on such a variety , if is strictly nef and , then is ample; we also show that if there exists a Cariter divisor in the boundary of the nef cone of , then contains a rational curve when its topological Euler characteristic is not .

Cite this article

Haidong Liu, Roberto Svaldi, Rational curves and strictly nef divisors on Calabi-Yau threefolds. Doc. Math. 27 (2022), pp. 1581–1604

DOI 10.4171/DM/904