Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting curves via degeneration   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.

32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an