Timeline for Moduli of smooth curves
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 18, 2023 at 18:09 | vote | accept | Bappa | ||
| Oct 16, 2023 at 13:16 | history | edited | Bappa | CC BY-SA 4.0 |
added 146 characters in body
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| Oct 16, 2023 at 12:07 | comment | added | Mikhail Katz | The closing votes on this question are unreasonable. It is easy to say that the result is true because the bigshots proved it long ago, but it does appear to be a nontrivial task to give an accessible explanation of this. Giving accessible explanations is of interest to research mathematicians and therefore legitimate on MO. | |
| Oct 16, 2023 at 8:45 | answer | added | Samir Canning | timeline score: 1 | |
| Oct 16, 2023 at 8:09 | answer | added | David Lehavi | timeline score: 2 | |
| Oct 15, 2023 at 21:14 | comment | added | Moishe Kohan | The easiest and most classical way to detect degeneration is by looking at a particular nonzero period and observe that it converges to zero as you move in a family of Riemann surfaces. Examples are easy to arrange by looking at hyperelliptic curves or at conformal connected sums of tori. | |
| Oct 15, 2023 at 15:02 | comment | added | Donu Arapura | There are already plenty of answers/comments addressing your question. But for general intuition, if you have some moduli space which parameterizes objects which can degenerate to an object outside the class you're dealing with, then this indicates the moduli space is not compact. | |
| Oct 15, 2023 at 12:58 | comment | added | Sam Nead | You need to improve the question by giving us a few hints about the background you want to assume. Which version of moduli space are you working with? What are its points, its topology? What background references are you comfortable with? And so on. | |
| Oct 15, 2023 at 12:17 | answer | added | Mikhail Katz | timeline score: 2 | |
| Oct 15, 2023 at 7:40 | answer | added | Sam Nead | timeline score: -1 | |
| Oct 14, 2023 at 19:00 | comment | added | Mikhail Katz | If one assumes the classical result that, for genus $g\geq2$, the moduli space of smooth curves is "the same" as the space of hyperbolic Riemann surfaces of genus $g$, then the noncompactness is easy to understand. A classical paper by Milnor shows that when one tends to infinity in the moduli space, the systole of the surface tends to zero (and vice versa). Of course this still leaves us with the task of actually constructing families of surfaces with systole tending to zero; this is a bit more complicated than the case of elliptic curves. | |
| Oct 14, 2023 at 15:08 | review | Close votes | |||
| Oct 22, 2023 at 3:03 | |||||
| Oct 14, 2023 at 14:37 | history | asked | Bappa | CC BY-SA 4.0 |