Cohomological invariants of complex manifolds coming from extremal rays

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dc.creatorWisniewski, Jaroslaw A.
dc.date1998-03-05
dc.date.accessioned2026-07-07T05:23:59Z
dc.date.available2026-07-07T05:23:59Z
dc.descriptionIn the present paper Mori extremal rays of a smooth projective manifold X are divided into two classes: L-supported and L-negligible (where ``L'' stands for ``Lefschetz'' since the division comes from Hard Lefschetz Theorem). Roughly speaking: L-supported rays are strongly distinguishable in topology while L-negligible rays have very mild geometry. Each L-supported ray R defines hyperplane in H^2(X,R) on which Lefschetz duality degenerates so it is a cohomology ring invariant. The hyperplane carries a multiplicity (cohomology ring invariant) which is related to the geometry of the ray R. The number of L-supported rays is bounded. Although the number of L-negligible rays may be infinite and they are invisible in the cohomology ring, their geometry is easier than that of L-supported rays. They are classifieable in low dimensions. Each L-negligible ray contains lots of ``good'' rational curves whose deformation is of expected dimension. In effect, L-negligible rays are invariant under deformations of complex structure and can be used to compute Gromov-Witten invariants in symplectic geometry.
dc.description16 pages, plain TeX
dc.identifierhttps://arxiv.org/abs/math/9803010
dc.identifierhttp://arxiv.org/abs/math/9803010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76662
dc.subjectAlgebraic Geometry
dc.titleCohomological invariants of complex manifolds coming from extremal rays
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