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Mar 25, 2022 at 5:35 comment added nolatos Thank you! I appreciate it.
Mar 25, 2022 at 4:15 comment added Kapil The family you have given is not flat as it is not equidimensional. In such contexts, flat implies equidimensional. Regarding your original question, the consequence of flatness and properness is that the direct image of a locally free sheaf is locally free.
Mar 25, 2022 at 3:41 history edited nolatos CC BY-SA 4.0
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Mar 25, 2022 at 2:24 history edited nolatos CC BY-SA 4.0
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Mar 25, 2022 at 2:04 history asked nolatos CC BY-SA 4.0