Timeline for Are the Chern numbers of a hyperbolic-type compact complex manifold bounded in terms of the Euler number?
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14 events
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| Feb 12, 2013 at 1:47 | history | edited | YangMills |
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| Feb 12, 2013 at 1:46 | comment | added | YangMills | Proposition 3.13 in this paper of Catanese-Schneider dx.doi.org/10.1007/BF01444736 gives universal bounds for the Chern numbers (assuming $K_X$ ample like you want) in terms of $(−1)^n c^n_1=K^n_X$. Does this help? When $n=3$, you also have the Yau inequality which bounds −$c^3_1\leq(8/3)(−c_1)c_2$, but then? | |
| Feb 11, 2013 at 20:35 | comment | added | YangMills | In this related question mathoverflow.net/questions/26586/… Dmitri points out that the answer is definitely NO if you drop the assumption of negative first Chern class. | |
| Feb 10, 2013 at 10:37 | comment | added | Ariyan Javanpeykar | Ow I misread your question. Thanks for the clarification. | |
| Feb 9, 2013 at 22:40 | comment | added | Vesselin Dimitrov | I ask about bounding the degree-$n$ combinations of the $c_i$ in terms of $c_n$. Now, $c_i$ has degree $i$. Since the only degree-$n$ combination involving $c_n$ is $c_n$ itself, I removed $i=n$ from the product. | |
| Feb 9, 2013 at 17:39 | comment | added | Ariyan Javanpeykar | Should your product be from $i=1$ until $i=n$, and your sum read $\sum_i k_i =n$? | |
| Feb 9, 2013 at 13:03 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 9, 2013 at 12:45 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 9, 2013 at 12:35 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 9, 2013 at 12:18 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 9, 2013 at 12:03 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 9, 2013 at 11:58 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 9, 2013 at 11:51 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 9, 2013 at 11:43 | history | asked | Vesselin Dimitrov | CC BY-SA 3.0 |