Timeline for What does it mean that $[X]+[Y]=0$ in the Grothendieck ring of varieties?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:30 | comment | added | Artur Jackson | Edited to include general proof strategy. | |
| Apr 13, 2017 at 12:30 | history | edited | Artur Jackson | CC BY-SA 3.0 |
added more of general idea
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| Apr 13, 2017 at 12:18 | comment | added | SashaP | For $\mathbb{C}$ the Hodge polynomial can be used instead. | |
| Apr 13, 2017 at 12:14 | comment | added | Artur Jackson | or better: $[X \cup Y] = [X] + [Y] = 0$. So then $X \cup Y$ is the empty variety. | |
| Apr 13, 2017 at 12:12 | comment | added | Artur Jackson | Perhaps: using semiring tactics? I think there is a more subtle version $K_0(Var/k)^+$ which is a semiring defined essentially the same way but with free semigroup and congruences. And try positivity? | |
| Apr 13, 2017 at 12:02 | comment | added | user2520938 | Thanks, that's nice and easy. Any ideas for the case $k=\mathbb{C}$? | |
| Apr 13, 2017 at 11:59 | history | answered | Artur Jackson | CC BY-SA 3.0 |