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Correnti positive: Uno strumento per l’analisi globale su varietà complesse

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Abstract

Lo scopo di questo testo è di presentare i temi principali riguardanti le correnti positive su varietà complesse. L’importanza di questo strumento, per coloro che studiano geometria complessa, è evidente; tuttavia non è semplice tenere le fila di una grande quantità di contributi sull’argomento, alcuni dei quali sono ormai pietre miliari su questa via. Vorremmo quindi delineare una “mappa” dei contributi che ci sono sembrati particolarmente significativi; per ovvie ragioni, rimandiamo ai test originali non appena si voglia entrare nel merito dei singoli argomenti.

Lo scritto è composto di due parti (oltre a una appendice dedicata al lettore che affronta per la prima volta il tema delle correnti positive): nella prima si trattano principalmente i temi in riferimento alle correnti positive e chiuse, storicamente la classe più importante di correnti per le varietà complesse, in quanto generalizzazione naturale delle sottovarietà. Nella seconda si espongono risultati su correntiT positive pluriarmoniche o plurisubarmoniche, cioè caratterizzate da una condizione imposta alla corrente\(i\partial \bar \partial T\), e naturali generalizzazioni delle funzioni plurisubarmoniche, nonché delle correnti chiuse. Questa scelta è motivata nel primo capitolo della seconda parte, partendo dall’ormai classico teorema di R. Harvey e J.R. Lawson che caratterizza tramite correnti positive e pluriarmoniche l’esistenza di metriche kähleriane su varietà compatte.

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  1. Dipartimento di Matematica dell’ Università di Parma, Via D’Azeglio 85, 43100, Parma

    Lucia Alessandrini

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  1. Lucia Alessandrini
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Conferenza tenuta il giorno 27 Aprile 1998

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Alessandrini, L. Correnti positive: Uno strumento per l’analisi globale su varietà complesse. Seminario Mat. e. Fis. di Milano 68, 59–120 (1998). https://doi.org/10.1007/BF02925830

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