Derived Kodaira Spencer map, Cosection lemma, and semiregularity

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dc.creatorChang, Huai-Liang
dc.date2008-08-07
dc.date2009-03-28
dc.date.accessioned2026-07-07T12:57:21Z
dc.date.available2026-07-07T12:57:21Z
dc.descriptionThe cosection lemma proved by J. Li and Y.H. Kiem said the intrinsic normal cone lies inside the kernel of any cosection of the obstruction sheaf when the moduli has a perfect obstruction theory. With a definition of higher tangent vectors of a scheme at a point, and a construction of the derived Kodaira Spencer map by K. Behrend and B. Fantechi, we prove a derived version of cosection lemma without perfect obstruction theory condition. As an application we give a short proof of the Kodaira's Principle \textit{ambient cohomology annihilates obstruction} (semiregularity), assuming the existence of locall universal family.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0808.0988
dc.identifierhttp://arxiv.org/abs/0808.0988
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224903
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject14D20
dc.titleDerived Kodaira Spencer map, Cosection lemma, and semiregularity
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