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Mar 30, 2018 at 12:50 comment added Jason Starr It is in Fulton's book, but it takes some time to say it in the "customary" fashion, because Fulton first carefully investigates the Chow groups additively before introducing intersection products. An alternative is Result 11.2.4 on p. 47 of Manin's notes, "Lectures on the K-Functor in Algebraic Geometry", iopscience.iop.org/article/10.1070/RM1969v024n05ABEH001357/meta
Mar 30, 2018 at 12:41 comment added Rene Schipperus Thank-you so much for this very interesting answer. There are some multiplicities in the original values that I supressed, the values for the first is $34$ as the double point lying on the plane counts as a two fold tangency. Also $140$ is the original number for the same reason. Where can I find the Grothendieck description of the Chow ring? Fulton ?
Mar 30, 2018 at 12:30 vote accept Rene Schipperus
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S Mar 30, 2018 at 7:03 history answered Jason Starr CC BY-SA 3.0
S Mar 30, 2018 at 7:03 history made wiki Post Made Community Wiki by Jason Starr