Timeline for Hypercube decomposition of perverse sheaves
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2013 at 17:04 | vote | accept | AFK | ||
| Nov 29, 2009 at 16:14 | comment | added | David Treumann | I added some references. If I now understand what Verdier specialization is, then by definition it differs from microlocalization just by a Fourier transform. I think the local system I am talking about will be present in the Fourier transforms of both the Verdier specialization and its vanishing part, possibly after shrinking our open set: if these two things differ by a relatively constant sheaf, then their Fourier transforms differ by something supported on the zero section. | |
| Nov 29, 2009 at 15:53 | history | edited | David Treumann | CC BY-SA 2.5 |
Sabbah
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| Nov 29, 2009 at 13:33 | comment | added | AFK | So we have 2 analogs of the vanishing cycles: - the vansihing part of the specialization on $T_ZX \setminus Z$ - the restriction of the microlocalization to $T^*_ZX \setminus Z$ I don't understand the relationship between the two. PS: do you have a good reference for your last paragraph on "blowup behaviors"? | |
| Nov 29, 2009 at 13:31 | comment | added | AFK | Verdier specialisation is exactly what you considered: the nearby cycles on the deformation to the normal cone (= normal bundle when the immersion is regular). It associates to a constructible sheaf, a monodromic sheaf on the normal bundle and $\nu_Z(F)|_{Z} = F|_Z$. Any monodromic sheaf has a decomposition into a relatively constant part (contant on the fibres) and a vanishing part (0 on the zero section). The restriction of the specialisation outside the zero section is the analog of the nearby cycles. The vanishing part of the specialization is the analog of the vanishing cycles. | |
| Nov 28, 2009 at 17:49 | history | answered | David Treumann | CC BY-SA 2.5 |