On the existence of curves in K-trivial threefolds

Details On the existence of curves in K-trivial threefolds On the existence of curves in K-trivial threefolds

1998-11-17

arxiv.org/abs/math/9811099v1

Mathematics

Algebraic Geometry

8 pages, LaTeX2e

Scientific paper

We give a criterion for a continuous family of curves on a nodal $K$-trivial
threefold $X_0$ to contribute geometrically rigid curves to a general smoothing
of $X_0$. As an application, we prove the existence of geometrically rigid
curves of arbitrary degree and explicitly bounded genus on general complete
intersection Calabi-Yau threefolds.

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