LEADER 02717nam 2200589 450 001 996466378603316 005 20220304153753.0 010 $a3-540-70519-8 024 7 $a10.1007/978-3-540-70519-2 035 $a(CKB)1000000000437221 035 $a(SSID)ssj0000316714 035 $a(PQKBManifestationID)11276945 035 $a(PQKBTitleCode)TC0000316714 035 $a(PQKBWorkID)10275484 035 $a(PQKB)10106577 035 $a(DE-He213)978-3-540-70519-2 035 $a(MiAaPQ)EBC3063148 035 $a(MiAaPQ)EBC6853012 035 $a(Au-PeEL)EBL6853012 035 $a(PPN)127054847 035 $a(EXLCZ)991000000000437221 100 $a20220304d2008 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aCompactifying moduli spaces for Abelian varieties /$fMartin C. Olsson 205 $a1st ed. 2008. 210 1$aBerlin, Heidelberg :$cSpringer-Verlag,$d[2008] 210 4$dİ2008 215 $a1 online resource (VIII, 286 p. 1 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-70518-X 320 $aIncludes bibliographical references and index. 327 $aA 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. 330 $aThis volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group. 410 0$aLecture Notes in Mathematics,$x0075-8434 606 $aAbelian varieties 606 $aModuli theory 615 0$aAbelian varieties. 615 0$aModuli theory. 676 $a516.353 700 $aOlsson$b Martin C.$0315787 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466378603316 996 $aCompactifying moduli spaces for Abelian varieties$9230597 997 $aUNISA