000 02472nam a22004098i 4500
001 CR9781316995846
003 UkCbUP
005 20200124160209.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 160725s2017||||enk o ||1 0|eng|d
020 _a9781316995846 (ebook)
020 _z9781108422628 (hardback)
020 _z9781316639566 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA564
_b.C28 2017
082 0 0 _a516.3/5
_223
100 1 _aCarlson, James A.,
_d1946-
_eauthor.
245 1 0 _aPeriod mappings and period domains /
_cJames Carlson, Stefan Müller-Stach, Chris Peters.
250 _aSecond edition.
264 1 _aCambridge :
_bCambridge University Press,
_c2017.
300 _a1 online resource (xiv, 562 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge studies in advanced mathematics ;
_v168
500 _aTitle from publisher's bibliographic system (viewed on 30 Aug 2017).
520 _aThis up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether-Lefschetz theorem and Nori's theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Kähler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford-Tate groups and their associated domains, the Mumford-Tate varieties and generalizations of Shimura varieties.
650 0 _aGeometry, Algebraic.
650 0 _aHodge theory.
650 0 _aTorelli theorem.
700 1 _aMüller-Stach, Stefan,
_d1962-
_eauthor.
700 1 _aPeters, Chris,
_eauthor.
776 0 8 _iPrint version:
_z9781108422628
830 0 _aCambridge studies in advanced mathematics ;
_v168.
856 4 0 _uhttps://doi.org/10.1017/9781316995846
999 _c515619
_d515617