Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SMOOTH, ISOLATED CURVES IN FAMILIES OF CALABI-YAU THREEFOLDS IN HOMOGENEOUS SPACES

  • Received : 2012.10.09
  • Published : 2013.09.01
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Abstract

We show the existence of smooth isolated curves of different degrees and genera in Calabi-Yau threefolds that are complete intersections in homogeneous spaces. Along the way, we classify all degrees and genera of smooth curves on BN general K3 surfaces of genus ${\mu}$, where $5{\leq}{\mu}{\leq}10$. By results of Mukai, these are the K3 surfaces that can be realised as complete intersections in certain homogeneous spaces.

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References

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Cited by

  1. Rational curves in CICYs in products of two projective spaces vol.45, pp.7, 2017, https://doi.org/10.1080/00927872.2016.1233228
  2. Brill–Noether general curves on Knutsen K3 surfaces vol.352, pp.2, 2014, https://doi.org/10.1016/j.crma.2013.11.020