Browsing by Subject "Quadric"
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Item Open Access On the number of components of a complete intersection of real quadrics(Springer Basel, 2012) Degtyarev, Alex; Itenberg, Ilia; Kharlamov, Viatchesla; Itenberg, I.; Jöricke, B.; Passare, M.Our main results concern complete intersections of three real quadrics. We prove that the maximal number B0 2 (N) of connected components that a regular complete intersection of three real quadrics in ℙN may have differs at most by one from the maximal number of ovals of the submaximal depth [(N −1)/2] of a real plane projective curve of degree d = N +1. As a consequence, we obtain a lower bound 1/4 N2 +O(N) and an upper bound 3/8 N2+O(N) for B0 2 (N). © Springer Science+Business Media, LLC 2012.Item Open Access Rigid isotopy classification of real algebraic curves of bidegree (3,3) on quadrics(M A I K Nauka - Interperiodica, 1999) Degtyarev, A. I.; Zvonilov, V. I.A rigid isotopy of nonsingular real algebraic curves on a quadric is a path in the space of such curves of a given bidegree. We obtain the rigid isotopy classification of nonsingular real algebraic curves of bidegree (3,3) on a hyperboloid and on an ellipsoid. We also study the space of real algebraic curves of bidegree (3, 3) with a single node or cusp. ©2000 Kluwer Academic/Plenum Publishers.