000147194 001__ 147194 000147194 005__ 20260112133357.0 000147194 0247_ $$2doi$$a10.2422/2036-2145.202111_014 000147194 0248_ $$2sideral$$a140976 000147194 037__ $$aART-2024-140976 000147194 041__ $$aeng 000147194 100__ $$aPopovici, Dan 000147194 245__ $$aHigher-page Hodge theory of compact complex manifolds 000147194 260__ $$c2024 000147194 5060_ $$aAccess copy available to the general public$$fUnrestricted 000147194 5203_ $$aOn a compact @ @-manifold X, one has the Hodge decomposition: the de Rham cohomology groups split into subspaces of pure-type classes as HkdR(X) = p+q=kHp;q(X), where the Hp;q(X) are canonically isomorphic to the Dolbeault cohomology groups Hp;q @ (X). For an arbitrary nonnegative integer r, we introduce the class of page-r-@ @-manifolds by requiring the analogue of the Hodge decomposition to hold on a compact complex manifold X when the usual Dolbeault cohomology groups Hp; q @ (X) are replaced by the spaces Ep; q r+1(X) featuring on the (r + 1)-st page of the Frolicher spectral sequence of X. The class of page-r-@ @-manifolds coincides with the usual class of @ @-manifolds when r = 0 but may increase as r increases. We give two kinds of applications. On the one hand, we give a purely numerical characterisation of the page-r-@ @-property in terms of dimensions of various cohomology vector spaces. On the other hand,we obtain several classes of examples, including all complex parallelisable nilmanifolds and certain families of solvmanifolds and abelian nilmanifolds. Further, there are general results about the behaviour of this new class under standard constructions like blow-ups and deformations. 000147194 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000147194 590__ $$a1.3$$b2024 000147194 592__ $$a1.775$$b2024 000147194 591__ $$aMATHEMATICS$$b71 / 483 = 0.147$$c2024$$dQ1$$eT1 000147194 593__ $$aTheoretical Computer Science$$c2024$$dQ1 000147194 593__ $$aMathematics (miscellaneous)$$c2024$$dQ1 000147194 594__ $$a2.3$$b2024 000147194 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000147194 700__ $$aStelzig, Jonas 000147194 700__ $$0(orcid)0000-0003-2207-8653$$aUgarte, Luis$$uUniversidad de Zaragoza 000147194 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000147194 773__ $$g25, 3 (2024), 1431–1464$$pAnn. sc. norm. super. Pisa, Cl. sci.$$tANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE$$x0391-173X 000147194 8564_ $$s442714$$uhttps://zaguan.unizar.es/record/147194/files/texto_completo.pdf$$yPostprint 000147194 8564_ $$s2416038$$uhttps://zaguan.unizar.es/record/147194/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000147194 909CO $$ooai:zaguan.unizar.es:147194$$particulos$$pdriver 000147194 951__ $$a2026-01-12-13:22:08 000147194 980__ $$aARTICLE