Geodesic
Complexity of intersections of real quadrics and topology of symmetric determinantal varieties
Journal of the European Mathematical Society, Tome 18 (2016) no. 2, pp. 353-379.

Voir la notice de l'article provenant de la source EMS Press

Let W be a linear system of quadrics on the real projective space RPn and X be the base locus of that system (i.e. the common zero set of the quadrics in W). We prove a formula relating the topology of X to the one of the discriminant locus ΣW​ (i.e. the set of singular quadrics in W). The set ΣW​ equals the intersection of W with the discriminant hypersurface for quadrics; its singularities are unavoidable (they might persist after a small perturbation of W) and we set {ΣW(r)​}r≥1​ for its singular point stratification, i.e. ΣW(1)​=ΣW​ and ΣW(r)​=Sing(ΣW(r−1)​). With this notation, for a generic W the mentioned formula writes:
DOI : 10.4171/jems/592
Classification : 14-XX, 55-XX
Keywords: Real algebraic geometry, real quadrics, homological compexity, determinantal varieties 
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     author = {Antonio Lerario},
     title = {Complexity of intersections of real quadrics and topology of symmetric determinantal varieties},
     journal = {Journal of the European Mathematical Society},
     pages = {353--379},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2016},
     doi = {10.4171/jems/592},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/592/}
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Antonio Lerario. Complexity of intersections of real quadrics and topology of symmetric determinantal varieties. Journal of the European Mathematical Society, Tome 18 (2016) no. 2, pp. 353-379. doi : 10.4171/jems/592. http://geodesic.mathdoc.fr/articles/10.4171/jems/592/

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