Smooth, isolated curves in families of Calabi-Yau threefolds in homogeneous spaces
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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 μ, where 5 ≤ μ ≤ 10. By results of Mukai, these are the K3 surfaces that can be realised as complete intersections in certain homogeneous spaces.
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 μ, where 5 ≤ μ ≤ 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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