Matches in SemOpenAlex for { <https://semopenalex.org/work/W3035636161> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W3035636161 abstract "Given a rational homogeneous manifold S=G/P of Picard number one and a Schubert variety S0 of S, the pair (S,S0) is said to be homologically rigid if any subvariety of S having the same homology class as S0 must be a translate of S0 by the automorphism group of S. The pair (S,S0) is said to be Schur rigid if any subvariety of S with homology class equal to a multiple of the homology class of S0 must be a sum of translates of S0. Earlier we completely determined homologically rigid pairs (S,S0) in case S0 is homogeneous and answered the same question in smooth non-homogeneous cases. In this article we consider Schur rigidity, proving that (S,S0) exhibits Schur rigidity whenever S0 is a non-linear smooth Schubert variety. Modulo a classification result of the first author’s, our proof proceeds by a reduction to homological rigidity by deforming a subvariety Z of S with homology class equal to a multiple of the homology class of S0 into a sum of distinct translates of S0, and by observing that the arguments for the homological rigidity apply since any two translates of S0 intersect in codimension at least two. Such a degeneration is achieved by means of the C∗-action associated with the stabilizer of the Schubert variety T0 opposite to S0. By transversality of general translates, a general translate of Z intersects T0 transversely and the C∗-action associated with the stabilizer of T0 induces a degeneration of Z into a sum of translates of S0, not necessarily distinct. After investigating the Bialynicki-Birular decomposition associated with the C∗-action we prove a refined form of transversality to get a degeneration of Z into a sum of distinct translates of S0." @default.
- W3035636161 created "2020-06-19" @default.
- W3035636161 creator A5016386280 @default.
- W3035636161 creator A5074582013 @default.
- W3035636161 date "2020-06-15" @default.
- W3035636161 modified "2023-10-01" @default.
- W3035636161 title "Schur rigidity of Schubert varieties in rational homogeneous manifolds of Picard number one" @default.
- W3035636161 cites W1480042721 @default.
- W3035636161 cites W1511019311 @default.
- W3035636161 cites W1536945458 @default.
- W3035636161 cites W1560269290 @default.
- W3035636161 cites W1579046653 @default.
- W3035636161 cites W1584561919 @default.
- W3035636161 cites W1863109379 @default.
- W3035636161 cites W1997717420 @default.
- W3035636161 cites W1998438394 @default.
- W3035636161 cites W1999529321 @default.
- W3035636161 cites W2002419186 @default.
- W3035636161 cites W2009424268 @default.
- W3035636161 cites W2013748928 @default.
- W3035636161 cites W2021503434 @default.
- W3035636161 cites W2023315059 @default.
- W3035636161 cites W2034441927 @default.
- W3035636161 cites W2050355762 @default.
- W3035636161 cites W2061340086 @default.
- W3035636161 cites W2068156293 @default.
- W3035636161 cites W2093199700 @default.
- W3035636161 cites W2160543918 @default.
- W3035636161 cites W2469827724 @default.
- W3035636161 cites W2493275345 @default.
- W3035636161 cites W2783846073 @default.
- W3035636161 cites W2962905070 @default.
- W3035636161 cites W2964051802 @default.
- W3035636161 cites W4231492974 @default.
- W3035636161 cites W4242128908 @default.
- W3035636161 doi "https://doi.org/10.1007/s00029-020-00571-9" @default.
- W3035636161 hasPublicationYear "2020" @default.
- W3035636161 type Work @default.
- W3035636161 sameAs 3035636161 @default.
- W3035636161 citedByCount "1" @default.
- W3035636161 countsByYear W30356361612022 @default.
- W3035636161 crossrefType "journal-article" @default.
- W3035636161 hasAuthorship W3035636161A5016386280 @default.
- W3035636161 hasAuthorship W3035636161A5074582013 @default.
- W3035636161 hasBestOaLocation W30356361612 @default.
- W3035636161 hasConcept C114614502 @default.
- W3035636161 hasConcept C121332964 @default.
- W3035636161 hasConcept C136119220 @default.
- W3035636161 hasConcept C160343418 @default.
- W3035636161 hasConcept C202444582 @default.
- W3035636161 hasConcept C33923547 @default.
- W3035636161 hasConcept C47158899 @default.
- W3035636161 hasConcept C62520636 @default.
- W3035636161 hasConcept C66882249 @default.
- W3035636161 hasConceptScore W3035636161C114614502 @default.
- W3035636161 hasConceptScore W3035636161C121332964 @default.
- W3035636161 hasConceptScore W3035636161C136119220 @default.
- W3035636161 hasConceptScore W3035636161C160343418 @default.
- W3035636161 hasConceptScore W3035636161C202444582 @default.
- W3035636161 hasConceptScore W3035636161C33923547 @default.
- W3035636161 hasConceptScore W3035636161C47158899 @default.
- W3035636161 hasConceptScore W3035636161C62520636 @default.
- W3035636161 hasConceptScore W3035636161C66882249 @default.
- W3035636161 hasIssue "3" @default.
- W3035636161 hasLocation W30356361611 @default.
- W3035636161 hasLocation W30356361612 @default.
- W3035636161 hasOpenAccess W3035636161 @default.
- W3035636161 hasPrimaryLocation W30356361611 @default.
- W3035636161 hasRelatedWork W1963642908 @default.
- W3035636161 hasRelatedWork W1970958630 @default.
- W3035636161 hasRelatedWork W2011083542 @default.
- W3035636161 hasRelatedWork W2088544526 @default.
- W3035636161 hasRelatedWork W2144457370 @default.
- W3035636161 hasRelatedWork W2583248246 @default.
- W3035636161 hasRelatedWork W2954160600 @default.
- W3035636161 hasRelatedWork W3035636161 @default.
- W3035636161 hasRelatedWork W3154129246 @default.
- W3035636161 hasRelatedWork W4300763502 @default.
- W3035636161 hasVolume "26" @default.
- W3035636161 isParatext "false" @default.
- W3035636161 isRetracted "false" @default.
- W3035636161 magId "3035636161" @default.
- W3035636161 workType "article" @default.