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Is there a "modern" account of Lefschetz proof of his theorem about $(1,1)$ classes for projective surfaces ?

I believe that would be very interesting to understand the original arguments and also a nice applications of pencils of curves. The sketch of Wikipedia is quite nice but I would love to see more details about the theorems by Poincaré and Lefschetz mentioned in the Wikipedia sketch.

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I like chapter 6 of

Lewis, James D. A survey of the Hodge conjecture, Second edition, Appendix B by B. Brent Gordon, CRM Monogr. Ser., 10, American Mathematical Society, Providence, RI, 1999.

It has lots of nice pictures too.

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  • $\begingroup$ I think this is exactly what I was looking for. $\endgroup$ Commented Mar 5 at 9:48

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