Counting curves via degeneration
Algebraic Geometry
2015-10-08 v3 Symplectic Geometry
Abstract
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. Also, we give a geometric construction of walls in the Gross-Siebert construction of Calabi-Yau varieties.
Cite
@article{arxiv.1108.2802,
title = {Counting curves via degeneration},
author = {Takeo Nishinou},
journal= {arXiv preprint arXiv:1108.2802},
year = {2015}
}
Comments
v2. Added references