Counting curves via degeneration

Details Counting curves via degeneration Counting curves via degeneration

2011-08-13

arxiv.org/abs/1108.2802v2

Mathematics

Algebraic Geometry

v2. Added references

Scientific paper

We develop a technique to study curves in a variety which has a degeneration into some union of varieties. The class of such varieties is very broad, but the theory becomes particularly useful when the variety has a degeneration into a union of toric varieties. Hypersurfaces are typical examples, and we study lines on K3 surfaces and quintic Calabi-Yau hypersurfaces in detail. In particular, we combinatorially prove the existence of 2875 lines in a generic quintic Calabi-Yau 3-fold.

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