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Dec 10, 2015 at 21:50 comment added Jason Starr The answer to both questions is "yes". You might Google "generic determinantal variety" or "generic determinantal ideal". This is a very classic subject. One more recent article is the article by Israel Vainsencher where he writes down a log resolution of the generic determinantal ideal and uses his resolution to compute (what are now called) the discrepancies of this ideal.
Dec 10, 2015 at 21:26 history edited user20948 CC BY-SA 3.0
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Dec 10, 2015 at 21:17 history asked user20948 CC BY-SA 3.0