Divisorial Zariski decompositions on compact complex manifolds

By S. Boucksom. 2004

344 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/43fb655f86a459b9e0770b97f87d77894b989839

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Citations in the corpus

Comparing numerical dimensions (2011, background): “The positive product (developed in [Boucksom 2004; Boucksom et al. 2012]) is a construction that encapsulates this approach to asymptotic behavior.”
Kähler currents and null loci (2013, methodology): “and non-Kähler loci were introduced by Boucksom [5], and they have been much studied recently in connection with the regularity for complex MongeAmpère equations in big cohomology classes [2, 7, 20].”
Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs (2013, background): “We will be very brief about this well-known notion, and refer e.g. to [ Bou04 , § 2.8], [ BBGZ13 , § 1], [ Ber09 ] or [ BD12 ] for more details and recent results.”
Lagrangian Fibrations of Holomorphic-Symplectic Varieties of K3[n]-Type (2013, background): “elongs to the closure of FEY. The class c1(L) is assumed nef, and hence belongs to the closure of FEX. The bimeromorphic map f induces a Hodge-isometry f∗ : H2(X,Z) → H2(Y,Z), which maps FEX onto FEY [Bou]. Hence, f∗(c1(L)) belongs to FEY as well. We conclude the equality f∗(c1(L)) = ψ−1(α). Let L2 ”
A variational approach to complex Monge-Ampère equations (2009, background): “. On the other hand for a general big class the existence of even a single θ-psh function with minimal singularities that is also C∞ on the ample locus Amp(θ) is unknown. For instance it follows from [Bou04] that no θ-psh function with minimal singularities will have analytic singularities unless {θ”
A survey of Torelli and monodromy results for holomorphic-symplectic varieties (2011, background): “. Part (2) of the theorem asserts that if a class αsatisﬁes the assumptions stated, then αis contained in FUX, if and only if it is contained in BKX. The ‘only if’ direction of part (2) is stated in ([Bou2], Theorem 4.3). The ‘if’ part is the obvious direction. Indeed, let f: X→ Y be a birational ma”
MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations (2013, positive): “ional classes Dwith D2 = 0 in the closure of the movable cone; such a Dis movable due to our proof of the Lagrangian ﬁbration conjec ture in Theorem 1.5. Using the divisorial Zariski decomposition of [Bou04], one can show for any hyperka¨hler variety that the pseudo-effective cone is dual to the clo”
Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, background): “The formal denition will not be reproduced here (the interested reader can protably consult the references [24], [ 4 ]), however, in order to gain some intuition about it, let us mention that if L has a Zariski decomposition, then num(L) is the familiar numerical dimension of the nef part.”