Timeline for Topological description of a blow up of a manifold along a submanifold
Current License: CC BY-SA 3.0
9 events
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| S Dec 8, 2017 at 13:15 | history | bounty ended | CommunityBot | ||
| S Dec 8, 2017 at 13:15 | history | notice removed | CommunityBot | ||
| Nov 30, 2017 at 18:03 | comment | added | Dan Petersen | This is also explained in Griffiths-Harris, Chapter 4, Section 6: "Blowing up a submanifold". In this section they compute the cohomology of a blow-up by a Mayer-Vietoris argument for the open cover given by $U = X \setminus Z$ and $V=$ a tubular neighborhood of the exceptional divisor in $\mathrm{Bl}_Z(X)$. | |
| Nov 30, 2017 at 14:59 | comment | added | HYL | The topological description of blow-ups is very well explained in McDuff's paper "Examples of simply-connected symplectic non-Kählerian manifolds"; see paragraph 2 and especially Definition 2.2. In that definition, $\tilde{V}$ is the neighborhood of the zero section of $\mathcal{O}_{\mathbf{P}(N_{Z/X})}(1)$, whose total space can be identified with $Y- S$ where $Y = \mathbf{P}(N_{Z/X} \oplus \mathcal{O}) $ and $S$ is the section of $Y \to Z$ corresponding to the quotient $N_{Z/X} \oplus \mathcal{O} \to \mathcal{O}$. So topologically $Bl_ZX$ is indeed a connected sum of $X$ with $Y$. | |
| S Nov 30, 2017 at 11:40 | history | bounty started | Saal Hardali | ||
| S Nov 30, 2017 at 11:40 | history | notice added | Saal Hardali | Canonical answer required | |
| Nov 27, 2017 at 23:50 | comment | added | user21574 | See arxiv.org/pdf/1210.1687.pdf , The proof of Lemma 2.7 math.leidenuniv.nl/scripties/pasquotto.pdf , also page 7 and 8 of Ruan paper arxiv.org/pdf/math/0611592.pdf is interesting also | |
| Nov 27, 2017 at 22:41 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Nov 27, 2017 at 21:03 | history | asked | Saal Hardali | CC BY-SA 3.0 |