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Journal Publications
| Citation key | B-Average-Euler-Characteristic-Of-Random-Real-Algebraic-Varieties |
|---|---|
| Author | Peter Bürgisser |
| Pages | 507-512 |
| Year | 2007 |
| Journal | Comptes Rendus - Mathematique |
| Volume | 345 |
| Number | 9 |
| Abstract | We determine the expected curvature polynomial of real projective varieties given as the zero set of independent random polynomials with Gaussian distribution, which is invariant under the orthogonal group. In particular, the expected Euler characteristic of such random real projective varieties is found. This considerably extends previously known results on the number of roots, the volume, and the Euler characteristic of the real solution set of random polynomial equations. |