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Sheldon KatsKatz, On the finiteness of rational curves on quintic threefolds, Compositio Math, 1986 60, 151-162 (1986) available from numdamas archive.numdam.org/article/CM_1986__60_2_151_0.pdf
A detailed treatment can be found in
Sheldon Kats, On the finiteness of rational curves on quintic threefolds, Compositio Math, 1986, available from numdam
A detailed treatment can be found in
Sheldon Katz, On the finiteness of rational curves on quintic threefolds, Compositio Math 60, 151-162 (1986) available as archive.numdam.org/article/CM_1986__60_2_151_0.pdf