Period mappings and period domains [EBook] / James Carlson, Stefan MüllerStach, Chris Peters.
Period mappings and period domains [EBook] / James Carlson, Stefan MüllerStach, Chris Peters.
This uptodate introduction to Griffiths' theory of period maps and period domains focusses on algebraic, grouptheoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes tha...
Personal Name(s):  Carlson, James A., (author) 

MüllerStach, Stefan, (author) / Peters, Chris, (author)  
Edition: 
Second edition. 
Imprint: 
Cambridge :
Cambridge University Press,
2017

Physical Description: 
1 online resource (xiv, 562 pages) 
Note: 
englisch 
ISBN: 
9781316639566 9781108422628 9781316995846 
Series Title: 
Cambridge studies in advanced mathematics ;
168 
Subject (LOC):  
Full Text 
This uptodate introduction to Griffiths' theory of period maps and period domains focusses on algebraic, grouptheoretic 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 higherdimensional algebraic varieties such as the NoetherLefschetz theorem and Nori's theorem. They explain differential geometric methods, leading up to proofs of Arakelovtype 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 grouptheoretic approach to Hodge structures is explained, leading to MumfordTate groups and their associated domains, the MumfordTate varieties and generalizations of Shimura varieties. 