Timeline for Degree of a morphism between affine varieties
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 20, 2022 at 15:34 | comment | added | H A Helfgott | On second thought, "maxdegree" might be a good name. Can anybody come up with an argument against it? | |
| Sep 20, 2022 at 15:21 | comment | added | red_trumpet | Maybe not relevant, but you might want to clarify what $\operatorname{deg}(0)$ is. If all $f_i$ are zero, the map does not appear to be "worse" than any other constant map, but with typical definitions, you end up with a negative degree (as opposed to degree $0$ for other constant maps). | |
| Sep 20, 2022 at 14:37 | comment | added | H A Helfgott | I think we'll settle for calling it "maximum degree" and denoting it my $\mdeg$, where \mdeg is defined as \textrm{mdeg}. Or is that not good? | |
| Sep 20, 2022 at 11:21 | comment | added | user483792 | (1) Yes. (2) maxdegree (one word). | |
| Sep 19, 2022 at 17:26 | comment | added | H A Helfgott | The other definition (for finite morphisms) is also algebraic, no? | |
| Sep 19, 2022 at 16:26 | comment | added | pinaki | Algebraic Degree? | |
| Sep 19, 2022 at 14:55 | comment | added | H A Helfgott | Maybe "polynomial degree" (poldeg)? | |
| Sep 19, 2022 at 14:54 | comment | added | H A Helfgott | Hm, that's not what was immediately brought to my mind by degree of definition. Someone else suggests "maximal degree", but that may be more confusing - suggesting that one is taking a maximum over the range or the domain, no? | |
| Sep 19, 2022 at 14:50 | comment | added | Will Sawin | The name is by analogy with "field of definition", which is also a minimum, not depending on a particular definition. (en.wikipedia.org/wiki/Field_of_definition). So for readers familiar with that concept you should be OK, but I agree it might be problematic for others. | |
| Sep 19, 2022 at 14:35 | comment | added | H A Helfgott | Hm. "Degree of definition" (degdef?) makes it sound like the degree depends on the definition, but it doesn't; we are taking a minimum of $\deg(\overline{f})$. | |
| Sep 19, 2022 at 14:32 | comment | added | Will Sawin | Perhaps "complexity" or "degree of definition"? | |
| Sep 19, 2022 at 14:20 | history | asked | H A Helfgott | CC BY-SA 4.0 |