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Calculating Euler characteristics

Calculating Euler characteristics

User56437 · Wed Sep 25, 2019 12:54 pm

Hello, I am trying to use Singular to calculate Euler characteristics of some affine varieties over the complex numbers. I did a few tests using the EulerAff command and am getting strange results. For example I tried the following (and various similar alterations like changing the field to Q or R, changing the floating point number, adding more variables ...):

ring r = (complex,100,j),(x,y,z),dp;
ideal I = x;
EulerAff(I);

This gives the result 2. But this should be calculating the Euler characteristic of the complex plane and so should be 1. Does anybody know what is going on here/how I can correct this issue?

Re: Calculating Euler characteristics

User56437 · Tue Oct 01, 2019 1:03 pm

So I ended up contacting the person who wrote the chern.lib library and they have corrected the code, which should be updated as well.

Re: Calculating Euler characteristics

hannes · Thu Oct 10, 2019 11:01 am

fix with git commit 29f72ad8f1379c65671fb9809ace7ac76fa0cd20
see https://www.singular.uni-kl.de:8002/tra ... a0cd20/git