Timeline for Flat map with reduced fibers.
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Jan 5, 2011 at 10:55 | comment | added | kaddar | Is the result realy true for open morphism? | |
| Jan 4, 2011 at 13:50 | comment | added | kaddar | It seems to me that the result is valid for $f:X\rightarrow S$ assumed to be open (or universally open in AG). For see this, we can argue as above on $Reg(S)$ by base change... | |
| Jan 4, 2011 at 8:11 | comment | added | kaddar | Thanks to Liu and Angelo for the good reference in EGA and Matsumara commutative algebra. Dear Angelo, in the second question, i want to know if a morphism with reduced fibers stay with reduced fibers after any base change $S'\rightarrow S$ between reduced complex spaces ? Liu say that the answer is yes because the notion of "geometrically reduced " and "reduced" agree in complex analytic geometric. | |
| Jan 4, 2011 at 7:58 | comment | added | kaddar | Dear Georges, Thank you for the partial answer (I found another reference for this (with smooth base) :satz 2.4 p.245 in "Deformation komplexer Raume "of Grauert-Kerner in Math.Ann 153). Can we deduce from the case of smooth base the general case by considering the base change given by the natural injection of the smooth part $Reg(S)$ in $S$ . We must then show that the fiber product of $X$ by $Reg(S)$ over $S$ is an open, dense and reduced subspace of $X$. I think that density is due to the flatness which preserve schematic density and reducedness is due to smooth base case.... | |
| Jan 3, 2011 at 20:12 | history | edited | Angelo | CC BY-SA 2.5 |
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| Jan 3, 2011 at 19:55 | history | edited | Angelo | CC BY-SA 2.5 |
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| Jan 3, 2011 at 19:44 | history | answered | Angelo | CC BY-SA 2.5 |