Timeline for How should the degree of a variety be defined in a weighted projective space?

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Nov 21, 2012 at 16:30	comment	added	Will Sawin		What line bundle do you think is appropriate to use? Maybe the point I'm making is that there is no good thing to define to equal $\mathcal L$.
Nov 21, 2012 at 9:57	comment	added	user2013		I am aware of the definition of Hilbert polynomial but I wonder where you use the condition $\mathcal{O}(n)\times\mathcal{O}(m)=\mathcal{O}(n+m)$.
Nov 21, 2012 at 5:33	comment	added	Will Sawin		Hilbert polynomial in its most general form comes from a proper scheme $X$, a coherent sheaf $\mathcal F$, a line bundle $\mathcal L$. Then Hilbert polynomial is defined to be $p(n)=\chi(\mathcal F\otimes \mathcal L^{\otimes n})$. If $\mathcal L$ is ample, then this is eventually equal to $\Gamma(X,\mathcal F\otimes \mathcal L^{\otimes n})$ by whatever vanishing theorem.
Nov 21, 2012 at 5:10	comment	added	user2013		Could you remind me of condition we need to have Hilbert polynomial?
Nov 21, 2012 at 2:57	history	answered	Will Sawin	CC BY-SA 3.0