Wirtinger numbers and holomorphic symplectic immersions

Verbitski, M. (2005) Wirtinger numbers and holomorphic symplectic immersions. Selecta Mathematica - New Series, 10(4), pp. 551-559. (doi: 10.1007/s00029-004-0268-7)

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For any subvariety of a compact holomorphic symplectic Kähler manifold, we define the symplectic Wirtinger number W(X). We show that W (X) ≤ 1 and the equality is reached if and only if the subvariety XCM is trianalytic, i.e. compatible with the hyperkähler structure on M. For a sequence X1 → X2 →...Xn → M of immersions of simple holomorphic symplectic manifolds, we show that W(X1) ≤ W (X2) ≤...≤ W(Xn).

Item Type:Articles
Glasgow Author(s) Enlighten ID:Verbitski, Dr Mikhail
Authors: Verbitski, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Selecta Mathematica - New Series
ISSN (Online):1420-9020

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
316541Hyperkaehler manifoldsMikhail VerbitskiEngineering & Physical Sciences Research Council (EPSRC)GR/R77773/01Mathematics