Algebraic cobordism revisited

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dc.creatorLevine, M.
dc.creatorPandharipande, R.
dc.date2006-05-08
dc.date.accessioned2026-07-07T07:14:01Z
dc.date.available2026-07-07T07:14:01Z
dc.descriptionWe define a cobordism theory in algebraic geometry based on normal crossing degenerations with double point singularities. The main result is the equivalence of double point cobordism to the theory of algebraic cobordism previously defined by Levine and Morel. Double point cobordism provides a simple, geometric presentation of algebraic cobordism theory. As a corollary, the Lazard ring given by products of projective spaces rationally generates all nonsingular projective varieties modulo double point degenerations. Double point degenerations arise naturally in relative Donaldson-Thomas theory. We use double point cobordism to prove all the degree 0 conjectures in Donaldson-Thomas theory: absolute, relative, and equivariant.
dc.description62 pages
dc.identifierhttps://arxiv.org/abs/math/0605196
dc.identifierhttp://arxiv.org/abs/math/0605196
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112699
dc.subjectAlgebraic Geometry
dc.subjectK-Theory and Homology
dc.titleAlgebraic cobordism revisited
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