Peter B. Gothen

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Using the L 2 norm of the Higgs field as a Morse function, we study the moduli spaces of U(p, q)-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no constraints on (p, q). A key step is the identification of the function's local minima as moduli spaces of holomorphic triples. In a companion paper [7](More)
Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reduc-tive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we(More)
We calculate the Betti numbers of moduli spaces of representations of a universal central extension of a surface group in the groups U (2; 1) and S U (2; 1). In order to obtain our results we use the identiication of this space with an appropriate mod-uli space of Higgs bundles and Morse theory, following Hitchin's programme 11]. This requires a careful(More)
We develop a complete Hitchin–Kobayashi correspondence for twisted pairs on a compact Riemann surface X. The main novelty lies in a careful study of the the notion of polystability for pairs, required for having a bijective correspondence between solutions to the Hermite–Einstein equations, on one hand, and polystable pairs, on the other. Our results allow(More)
A holomorphic triple over a compact Riemann surface consists of two holo-morphic vector bundles and a holomorphic map between them. After fixing the topo-logical types of the bundles and a real parameter, there exist moduli spaces of stable holomorphic triples. In this paper we study non-emptiness, irreducibility, smoothness, and birational descriptions of(More)
a Ciência e a Tecnologia (Portugal) through the Centro de Matemática da Universidade do Porto and through grant no. SFRH/BPD/1606/2000. Abstract. Using the L 2 norm of the Higgs field as a Morse function, we study the moduli spaces of U(p, q)-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no(More)
Nous démontrons qu'uné economie d'´ echange (définie par ses préfé-rences et ses dotations) qui génère une fonction de demande excéden-taire aggrégée (DEA) z est proche de l'´ economie associéè a la DEA z , perturbation arbitraire de z. Abstract We establish that an exchange economy, i.e., preferences and endowments , that generates a given aggregate excess(More)