Geodesic
Rational curves and strictly nef divisors on Calabi-Yau threefolds
Documenta mathematica, Tome 27 (2022), pp. 1581-1604.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We give a criterion for a nef divisor $D$ to be semi-ample on a Calabi-Yau threefold $X$ when $D^3=0=c_2(X)\cdot D$ and $c_3(X)\neq 0$. As a direct consequence, we show that on such a variety $X$, if $D$ is strictly nef and $\nu(D)\neq 1$, then $D$ is ample; we also show that if there exists a Cariter divisor $D\not\equiv 0$ in the boundary of the nef cone of $X$, then $X$ contains a rational curve when its topological Euler characteristic is not $0$.
Classification : 14J32, 14E30, 14J30
Keywords: rational curves, strictly nef divisors, Calabi-Yau threefolds 
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     author = {Liu, Haidong and Svaldi, Roberto},
     title = {Rational curves and strictly nef divisors on {Calabi-Yau} threefolds},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a27/}
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Liu, Haidong; Svaldi, Roberto. Rational curves and strictly nef divisors on Calabi-Yau threefolds. Documenta mathematica, Tome 27 (2022), pp. 1581-1604. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a27/