Restriction theorems for homogeneous bundles

V. B. Mehta; V. Trivedi

doi:10.1016/j.bulsci.2006.06.001

Restriction theorems for homogeneous bundles

V. B. Mehta
, V. Trivedi

Mathematics

Tata Institute of Fundamental Research

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove that for an irreducible representation τ : GL (n) → GL (W), the associated homogeneous P_kⁿ-vector bundle W_τ is strongly semistable when restricted to any smooth quadric or to any smooth cubic in P_kⁿ, where k is an algebraically closed field of characteristic ≠ 2, 3 respectively. In particular W_τ is semistable when restricted to general hypersurfaces of degree ≥ 2 and is strongly semistable when restricted to the generic hypersurface of degree ≥ 2.

Original language	English
Pages (from-to)	397-404
Number of pages	8
Journal	Bulletin des Sciences Mathematiques
Volume	131
Issue number	4
DOIs	https://doi.org/10.1016/j.bulsci.2006.06.001
State	Published - Jun 2007

Access to Document

10.1016/j.bulsci.2006.06.001

Cite this

@article{582b05dcb8ac49d38b65ae0b93586b4b,

title = "Restriction theorems for homogeneous bundles",

abstract = "We prove that for an irreducible representation τ : GL (n) → GL (W), the associated homogeneous Pkn-vector bundle Wτ is strongly semistable when restricted to any smooth quadric or to any smooth cubic in Pkn, where k is an algebraically closed field of characteristic ≠ 2, 3 respectively. In particular Wτ is semistable when restricted to general hypersurfaces of degree ≥ 2 and is strongly semistable when restricted to the generic hypersurface of degree ≥ 2.",

author = "Mehta, \{V. B.\} and V. Trivedi",

year = "2007",

month = jun,

doi = "10.1016/j.bulsci.2006.06.001",

language = "English",

volume = "131",

pages = "397--404",

journal = "Bulletin des Sciences Mathematiques",

issn = "0007-4497",

publisher = "Elsevier Masson s.r.l.",

number = "4",

}

TY - JOUR

T1 - Restriction theorems for homogeneous bundles

AU - Mehta, V. B.

AU - Trivedi, V.

PY - 2007/6

Y1 - 2007/6

N2 - We prove that for an irreducible representation τ : GL (n) → GL (W), the associated homogeneous Pkn-vector bundle Wτ is strongly semistable when restricted to any smooth quadric or to any smooth cubic in Pkn, where k is an algebraically closed field of characteristic ≠ 2, 3 respectively. In particular Wτ is semistable when restricted to general hypersurfaces of degree ≥ 2 and is strongly semistable when restricted to the generic hypersurface of degree ≥ 2.

AB - We prove that for an irreducible representation τ : GL (n) → GL (W), the associated homogeneous Pkn-vector bundle Wτ is strongly semistable when restricted to any smooth quadric or to any smooth cubic in Pkn, where k is an algebraically closed field of characteristic ≠ 2, 3 respectively. In particular Wτ is semistable when restricted to general hypersurfaces of degree ≥ 2 and is strongly semistable when restricted to the generic hypersurface of degree ≥ 2.

UR - https://www.scopus.com/pages/publications/34249076759

U2 - 10.1016/j.bulsci.2006.06.001

DO - 10.1016/j.bulsci.2006.06.001

M3 - Article

AN - SCOPUS:34249076759

SN - 0007-4497

VL - 131

SP - 397

EP - 404

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

IS - 4

ER -

Restriction theorems for homogeneous bundles

Abstract

Access to Document

Other files and links

Fingerprint

Cite this