Timeline for Isomorphic equivariant sheaves are equivariantly isomorphic on a toric variety
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 23, 2018 at 0:38 | vote | accept | Walter Simon | ||
| Sep 20, 2018 at 12:54 | history | edited | Jason Starr | CC BY-SA 4.0 |
added 1242 characters in body
|
| Sep 20, 2018 at 12:40 | history | edited | Jason Starr | CC BY-SA 4.0 |
added 1242 characters in body
|
| Sep 20, 2018 at 11:51 | history | edited | Jason Starr | CC BY-SA 4.0 |
added 118 characters in body
|
| Sep 20, 2018 at 11:25 | history | edited | Jason Starr | CC BY-SA 4.0 |
added 161 characters in body
|
| Sep 20, 2018 at 11:17 | history | edited | Jason Starr | CC BY-SA 4.0 |
added 161 characters in body
|
| Sep 20, 2018 at 10:28 | history | edited | Jason Starr | CC BY-SA 4.0 |
added 238 characters in body
|
| Sep 20, 2018 at 9:42 | history | edited | Jason Starr | CC BY-SA 4.0 |
added 238 characters in body
|
| Sep 20, 2018 at 9:18 | comment | added | Jason Starr | @S.carmeli Yes, even when $X$ is not factorial, such an isomorphism induces an isomorphism of the reflexive hulls of $F_1$ and $F_2$. Moreover, the isomorphism induces an isomorphism between the quotient of the reflexive hull of $F_i$ by $F_i$. So it suffices to analyze different $T$-linearizations of reflexive, rank $1$ coherent sheaves on $X$. Since each of these restricts to a $T$-linearization of the structure sheaf on $T$, these are faithfully encoded by characterst of $T$. | |
| Sep 20, 2018 at 7:43 | comment | added | S. carmeli | Let me just comment that it is true, however, that $F_1\cong F_2 \otimes \chi$ for some character of the torus. This is because the isomorphism $F_1\cong F_2$ restricts to an isomorphism of the structure sheaf on $T$ as both $F_1$ and $F_2$ are isomorphic to the structure sheaf on $T$, and every such iso. is multiplication by invertible fuction, hence automatically aigen with respect to some character. | |
| S Sep 20, 2018 at 7:10 | history | answered | Jason Starr | CC BY-SA 4.0 | |
| S Sep 20, 2018 at 7:10 | history | made wiki | Post Made Community Wiki by Jason Starr |