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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Period Mappings and Period Domains (Paperback, 2nd Revised edition)
Loot Price: R1,692
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Period Mappings and Period Domains (Paperback, 2nd Revised edition)
Series: Cambridge Studies in Advanced Mathematics
Expected to ship within 12 - 17 working days
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This 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 Kahler. 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.
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