Timeline for Is the Euler characteristic a birational invariant
Current License: CC BY-SA 2.5
5 events
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| Jul 14, 2022 at 10:43 | comment | added | The Amplitwist |
The link to eom.springer.de is broken, but the article can now be found at encyclopediaofmath.org/wiki/Arithmetic_genus.
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| Sep 28, 2015 at 19:01 | comment | added | adrido | @Emerton: Dear Matt, I'm confused. If we normalize a nodal cubic, we get a smooth curve of geometric and arithmetic genus 0. But in the original curve, the arithmetic and the geometric genus are not the same: en.wikipedia.org/wiki/Genus%E2%80%93degree_formula. In fact, it's mentioned here en.wikipedia.org/wiki/Geometric_genus that the geometric genus is a birational invariant. So the arithmetic one cannot be. I don't know how much I can trust the wikipedia article but the fact that geometric genus is a birational invariant makes sense to me (e.g. a pinched sphere has genus 0). | |
| May 25, 2010 at 20:46 | comment | added | Ariyan Javanpeykar | False alarm. It's written in Hirzebruch's book on page 176. | |
| May 25, 2010 at 20:42 | comment | added | Ariyan Javanpeykar | Yes, I read that article too. Since I'm only interested in the characteristic zero case this does confirm that it's true. It's just that I would like to see "why" it is true. I looked through the Hirzebruch's book referred to in Dolgachev's article and couldn't find it. | |
| May 25, 2010 at 20:28 | history | answered | Emerton | CC BY-SA 2.5 |