Rank 3 rigid representations of projective fundamental groups
| Autor: | Carlos Simpson, Adrian Langer |
|---|---|
| Přispěvatelé: | Institute of Mathematics, Polish Academy of Sciences, Polska Akademia Nauk = Polish Academy of Sciences (PAN), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), ANR-13-PDOC-0015,TOFIGROU,Torseurs, fibrés vectoriels et schéma en groupes fondamental(2013), ANR-16-CE40-0011,Hodgefun,Groupes fondamentaux, Théorie de Hodge et Motifs(2016) |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Fundamental group Rank (differential topology) 01 natural sciences Higgs bundle 14F35 (primary) 14D06 14D07 14E20 (secondary) Mathematics - Algebraic Geometry Factorization 0103 physical sciences FOS: Mathematics Variation of Hodge structure 0101 mathematics Projective test Representation (mathematics) Algebraic Geometry (math.AG) Projective variety Mathematics Algebra and Number Theory 010102 general mathematics Representation Rigidity Irreducible representation [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 010307 mathematical physics |
| Zdroj: | Compositio Mathematica Compositio Mathematica, Foundation Compositio Mathematica, 2018, 154 (7), pp.1534-1570. ⟨10.1112/S0010437X18007182⟩ |
| ISSN: | 1570-5846 0010-437X |
| DOI: | 10.1112/s0010437x18007182 |
| Popis: | Let X be a smooth complex projective variety with basepoint x. We prove that every rigid integral irreducible representation $\pi_1(X,x)\to SL (3,{\mathbb C})$ is of geometric origin, i.e., it comes from some family of smooth projective varieties. This partially generalizes an earlier result by K. Corlette and the second author in the rank 2 case and answers one of their questions. Comment: v3, 49 pages; final version, to appear in Compositio Math |
| Databáze: | OpenAIRE |
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