The even Clifford structure of the fourth Severi variety

• Autorzy: Maurizio Parton , Paolo Piccinni
• Języki publikacji: 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.

Słowa kluczowe

EN

Clifford structure; exceptional symmetric space; octonions; canonical differential form

Kategorie tematyczne

• 53C38: Calibrations and calibrated geometries
• 53C26: Hyper-K\"ahler and quaternionic K\"ahler geometry, ``special'' geometry
• 53C27: Spin and Spin c geometry

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2015
• Tom: 2
• Numer: 1

Daty

otrzymano

2015-06-17

zaakceptowano

2015-07-22

online

2015-08-04

Twórcy

autor

Maurizio Parton

• Universit`a di Chieti-Pescara, Dipartimento di Economia, viale della Pineta 4, I-65129 Pescara, Italy

autor

Paolo Piccinni

• Sapienza-Universit`a di Roma, Dipartimento di Matematica, piazzale Aldo Moro 2,
  I-00185, Roma, Italy

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Identyfikatory

DOI

10.1515/coma-2015-0008