Compatibly Frobenius split subschemes are rigid

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dc.creatorKnutson, Allen
dc.date2009-01-15
dc.date.accessioned2026-07-07T12:29:38Z
dc.date.available2026-07-07T12:29:38Z
dc.descriptionSchwede proved very recently in arXiv:0901.1154 that in a quasiprojective scheme X with a fixed Frobenius splitting, there are only finitely many subschemes {Y} that are compatibly split. (A simpler proof has already since been given in arXiv:0901.2098, by Kumar and Mehta.) It follows that their deformations (as compatibly split subschemes) are obstructed. We give a short proof that if X is projective, its compatibly split subschemes {Y} have no deformations at all (again, as compatibly split subschemes). This reproves Schwede's result in some simple cases.
dc.description3 pages
dc.identifierhttps://arxiv.org/abs/0901.2188
dc.identifierhttp://arxiv.org/abs/0901.2188
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215942
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject13A35; 14A10
dc.titleCompatibly Frobenius split subschemes are rigid
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