02717nam 2200589 450 99646637860331620220304153753.03-540-70519-810.1007/978-3-540-70519-2(CKB)1000000000437221(SSID)ssj0000316714(PQKBManifestationID)11276945(PQKBTitleCode)TC0000316714(PQKBWorkID)10275484(PQKB)10106577(DE-He213)978-3-540-70519-2(MiAaPQ)EBC3063148(MiAaPQ)EBC6853012(Au-PeEL)EBL6853012(PPN)127054847(EXLCZ)99100000000043722120220304d2008 uy 0engurnn|008mamaatxtccrCompactifying moduli spaces for Abelian varieties /Martin C. Olsson1st ed. 2008.Berlin, Heidelberg :Springer-Verlag,[2008]©20081 online resource (VIII, 286 p. 1 illus.) Lecture Notes in Mathematics,0075-8434Bibliographic Level Mode of Issuance: Monograph3-540-70518-X Includes bibliographical references and index.A Brief Primer on Algebraic Stacks -- Preliminaries -- Moduli of Broken Toric Varieties -- Moduli of Principally Polarized Abelian Varieties -- Moduli of Abelian Varieties with Higher Degree Polarizations -- Level Structure.This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.Lecture Notes in Mathematics,0075-8434Abelian varietiesModuli theoryAbelian varieties.Moduli theory.516.353Olsson Martin C.315787MiAaPQMiAaPQMiAaPQBOOK996466378603316Compactifying moduli spaces for Abelian varieties230597UNISA