I have a surface over a field $k$ (of char 0) given by a conic bundle $y^2 - a z^2 = s(x)$, where I have $s(x)$ explicitly (but it depends also on some parameter). How can I compute its hodge numbers? I'm clueless on how to even begin! Any strategy, examples, etc are very welcome. Thank you.
2026-05-16 06:26:08.1778912768
Computing Hodge diamond
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