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The even Clifford structure of the fourth Severi variety

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Warianty tytułu
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EN
Abstrakty
EN
TheHermitian symmetric spaceM = EIII appears in the classification of complete simply connected Riemannian manifolds carrying a parallel even Clifford structure [19]. This means the existence of a real oriented Euclidean vector bundle E over it together with an algebra bundle morphism φ : Cl0(E) → End(TM) mapping Ʌ2E into skew-symmetric endomorphisms, and the existence of a metric connection on E compatible with φ. We give an explicit description of such a vector bundle E as a sub-bundle of End(TM). From this we construct a canonical differential 8-form on EIII, associated with its holonomy Spin(10) · U(1) ⊂ U(16), that represents a generator of its cohomology ring. We relate it with a Schubert cycle structure by looking at EIII as the smooth projective variety V(4) ⊂ CP26 known as the fourth Severi variety.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2015-06-17
zaakceptowano
2015-07-22
online
2015-08-04
Twórcy
  • Universit`a di Chieti-Pescara, Dipartimento di Economia, viale della Pineta 4, I-65129 Pescara, Italy
  • Sapienza-Universit`a di Roma, Dipartimento di Matematica, piazzale Aldo Moro 2,
    I-00185, Roma, Italy
Bibliografia
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  • [19] A. Moroianu and U. Semmelmann. Clifford structures on Riemannian manifolds. Adv. Math., 228(2):940–967, 2011.
  • [20] L. Ornea, M. Parton, P. Piccinni, and V. Vuletescu. Spin(9) geometry of the octonionic Hopf fibration. Transformation Groups,18(3):845–864, 2013.
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  • [22] M. Parton and P. Piccinni. Spin(9) and almost complex structures on 16-dimensional manifolds. Ann. Global Anal. Geom.,41(3):321–345, 2012.
  • [23] M. Parton and P. Piccinni. Spheres with more than 7 vector fields: All the fault of Spin(9). Linear Algebra Appl., 438(3):1113–1131, 2013.
  • [24] M. Radeschi. Clifford algebras and new singular Riemannian foliations in spheres. Geom. Funct. Anal., 24(5):1660–1682,2014.[WoS][Crossref]
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  • [27] F. Severi. Intorno ai punti doppi impropri di una superficie generale dello spazio a quattro dimensioni, e a’ suoi punti tripliapparenti. Palermo Rend., 15:33–51, 1901.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_coma-2015-0008
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