Timeline for Typo in a paper definition of Schubert cells?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 18, 2019 at 14:30 | comment | added | darij grinberg | @SebastianK.: Yes, their definition is a Schubert cell, while yours is the corresponding Schubert variety (i.e., the Zariski closure of the Schubert cell). I think the definitions are fairly standard, except that most authors use the standard basis instead of the eigenbasis of $A$ (of course, the difference is insubstantial, since any basis can be transformed into any other by an automorphism of the vector space), and that some authors use row-equivalence classes of $r\times n $-matrices instead of vector subspaces (but again, this is in bijection). | |
| Jan 18, 2019 at 14:21 | comment | added | Sebastian K. | At least, if I am not mistaken, the set $S_\pi$ (my lower definition) is the closure of the correct $S_\pi$ (as defined by the authors). So their definition should in fact be a Schubert cell, while mine is the Schubert variety. It seems like (English) Wikipedia is again not the best source, since their definition of Schubert cells seems to be the one of Schubert variety instead. I am not yet sure how distinguished those two definitions are in this field of mathematics... | |
| Jan 18, 2019 at 11:31 | vote | accept | Sebastian K. | ||
| Jan 18, 2019 at 11:31 | comment | added | Sebastian K. | I feel so embarrassed... thank you. | |
| Jan 18, 2019 at 11:17 | history | undeleted | darij grinberg | ||
| Jan 18, 2019 at 11:17 | history | edited | darij grinberg | CC BY-SA 4.0 |
deleted 14 characters in body
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| Jan 18, 2019 at 11:11 | history | deleted | darij grinberg | via Vote | |
| Jan 18, 2019 at 11:11 | history | answered | darij grinberg | CC BY-SA 4.0 |