Browsing by Author "Itenberg, I."

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    Deformation finiteness for real hyperkahler manifolds
    (Nezavisimyi Moskovskii Universitet, Independent University of Moscow, 2007-04) Degtyarev, A.; Itenberg, I.; Kharlamov, V.
    We show that the number of equivariant deformation classes of real structures in a given deformation class of compact hyperkahler manifolds is finite.
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    Finiteness and quasi-simplicity for symmetric K3-surfaces
    (Duke University Press, 2004) Degtyarev, A.; Itenberg, I.; Kharlamov, V.
    We compare the smooth and deformation equivalence of actions of finite groups on K3-surfaces by holomorphic and antiholomorphic transformations. We prove that the number of deformation classes is finite and, in a number of cases, establish the expected coincidence of the two equivalence relations. More precisely, in these cases we show that an action is determined by the induced action in the homology. On the other hand, we construct two examples to show first that, in general, the homological type of an action does not even determine its topological type, and second that K3-surfaces X and X̄ with the same Klein action do not need to be equivariantly deformation equivalent even if the induced action on H2,0(X) is real, that is, reduces to multiplication by ±1.
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    Lines on quartic surfaces
    (Springer, 2017) Degtyarev, A.; Itenberg, I.; Sertöz, A.S.
    We show that the maximal number of (real) lines in a (real) nonsingular spatial quartic surface is 64 (respectively, 56). We also give a complete projective classification of all quartics containing more than 52 lines: all such quartics are projectively rigid. Any value not exceeding 52 can appear as the number of lines of an appropriate quartic. © 2016, Springer-Verlag Berlin Heidelberg.
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    On total reality of meromorphic functions
    (Association des Annales de l ' Institut Fourier, 2007) Degtyarev, A.; Ekedahl, T.; Itenberg, I.; Shapiro, B.; Shapiro, M.
    We show that, if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points, then it is conjugate to a real meromorphic function by a suitable projective automorphism of the image.
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    Planes in cubic fourfolds
    (European Mathematical Society Publishing House, 2023) Degtyarev, Alex; Itenberg, I.; Ottem, J. C.
    We show that the maximal number of planes in a complex smooth cubic fourfold in P5 is 405, realized by the Fermat cubic only; the maximal number of real planes in a real smooth cubic fourfold is 357, realized by the so-called Clebsch–Segre cubic. Altogether, there are but three (up to projective equivalence) cubics with more than 350 planes © 2023,Algebraic Geometry. All Rights Reserved.
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    Real algebraic curves with large finite number of real points
    (Springer, 2019) Brugalle, E.; Degtyarev, Alex; Itenberg, I.; Mangolte, F.
    We address the problem of the maximal finite number of real points of a real algebraic curve (of a given degree and, sometimes, genus) in the projective plane. We improve the known upper and lower bounds and construct close to optimal curves of small degree. Our upper bound is sharp if the genus is small as compared to the degree. Some of the results are extended to other real algebraic surfaces, most notably ruled.