• Login
    View Item 
    •   Athenaeum Home
    • University of Georgia Theses and Dissertations
    • University of Georgia Theses and Dissertations
    • View Item
    •   Athenaeum Home
    • University of Georgia Theses and Dissertations
    • University of Georgia Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Results on an extended Torelli map and singularities of degenerate abelian varieties

    Thumbnail
    Date
    2014-05
    Author
    Tenini, Joseph Anthony
    Metadata
    Show full item record
    Abstract
    The Torelli map associates to a smooth genus g projective curve a g-dimensional principally polarized abelian variety and is a map on the respective moduli spaces Mg -> Ag. There is a somewhat canonical compacti fication of Mg, the Deligne-Mumford compactifi cation, but there are many natural compacti fications of Ag. In this thesis we consider two toroidal compacti fications, the central cone compacti fication and the second Voronoi compactification. Speci fically, we answer the following two questions: Does the Torelli map extend to a regular map to the central cone compactification in genera 7 and 8? What singularities occur on pairs in the image of the extended Torelli map to the second Voronoi compactification? The fi rst question is important because genera 7 and 8 represented the only remaining cases in which this particular extension question was unknown. The result, which is a product of joint work, is that the map does extend in these cases. The second question seeks to extend the 1995 result of Koll ar which states that principally polarized abelian pairs are log canonical. In this thesis we show that in fact all pairs in the boundary of the second Voronoi compactification are semi-log canonical, the analog of log canonical in the non-normal setting.
    URI
    http://purl.galileo.usg.edu/uga_etd/tenini_joseph_a_201405_phd
    http://hdl.handle.net/10724/30676
    Collections
    • University of Georgia Theses and Dissertations

    About Athenaeum | Contact Us | Send Feedback
     

     

    Browse

    All of AthenaeumCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister

    About Athenaeum | Contact Us | Send Feedback