Timeline for intersection and self intersection on non compact complex surfaces
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 19, 2021 at 8:15 | comment | added | singularity | thanks for your answer, but i don't see how a subvariety defines a class in the cohomology group i will try to study more about the poincaré duality, i a also would like to know if that intersection correcponds to the intersection multiplicity. for example let's take to subvariety $A$ et $B$ which meet at a point $x$ and suppose their local equation are f=0 and g=0 ( f and g are holomorphic function) can i say that $(A,B)_x = dis /frac{/mathbb{C}{x,y}}{(f,g)}$ ? | |
| May 19, 2021 at 6:58 | comment | added | Jonny Evans | A (compact respectively non-compact) subvariety defines a Poincaré dual class in (ordinary respectively compactly supported) cohomology. You can think of it using whatever model of cohomology you prefer. Intersection then corresponds to cup product of cohomology classes. Of course the answer is just a (compactly supported) cohomology class, but if the subvarieties have complementary dimension then you get a number by integrating over the ambient variety. | |
| May 18, 2021 at 19:11 | comment | added | singularity | I still don't understand even though i tried to read the book you suggested, i want to do intersecting between two divisor ( such that one of them is compactly supported ) but i don't the link with the intersection between forms is there somme sort of bijection between compactly suuported divisor on a complex surfaces $X$ and the de rahm cohomology group $H^{2}_c(X)$ ? | |
| May 17, 2021 at 14:46 | vote | accept | singularity | ||
| May 17, 2021 at 10:18 | history | answered | Jonny Evans | CC BY-SA 4.0 |