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Results tagged with euler-characteristics
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user 2900
3
votes
0
answers
167
views
Is there some short formula for the "defect" of Hilbert function
Let $X\subset\Bbb P^n_{\Bbb C}$ be a connected, Cohen Macaulay sub-scheme. (Possibly singular, reducible or non-reduced.) For $k\gg0$ the numbers $h^0(\mathcal{O}_X(k))$ depend polynomially on $k$. De …
- 2,232
3
votes
1
answer
680
views
Higher Euler characteristics (possible generalizations)
Let $X$ be projective and Gorenstein (over $\mathbb{C}$), of dimension $n$, then $\chi(\mathcal{O}_X)=(-1)^n\chi(\omega_X)$. Hence a "generalization": $\chi(\omega^{\otimes k}_X)$.
I'd like somethin …
- 2,232