Timeline for normal flatness and canonical bundle
Current License: CC BY-SA 2.5
6 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 5, 2011 at 7:10 | vote | accept | Franz | ||
| Mar 23, 2011 at 5:49 | comment | added | Sándor Kovács | Hi Franz, this sounds plausible, but I am a little doubtful that you would get such a simple formula in general. However, it seems to work for hypersurfaces. | |
| Mar 22, 2011 at 22:37 | comment | added | Franz | Thus I wondered if there were also a formula in this case. | |
| Mar 22, 2011 at 22:37 | comment | added | Franz | Dear Sandros, I really thank you for your detailed answer. In fact, as your example shows, when X is a hypersurface and X is equimultiple along Y (which is equivalent to normal flatness for hypersurfaces) there seems to be a formula K_Z = p^*K_X + (n-d)E (d is the multiplicity of X along Y and n the codimension of Y in X). In fact I know this formula is true if Y is a point and X is a hypersurface. I am pretty sure it is true if X is a hypersurface equimultiple along Y and Y is smooth. When X is no longer a hypersurface, a good replacement for equimultiplicity is normal flatness. | |
| Mar 22, 2011 at 22:25 | history | answered | Sándor Kovács | CC BY-SA 2.5 |