2011/08/13 by Nishinou, Takeo
#Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1108.2802
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.