Twisted symmetric differentials and the quadric algebra of subvarieties of $$\mathbb {P}^N$$ P N of low codimension

2018 ◽  
Vol 5 (2) ◽  
pp. 454-475
Author(s):  
Bruno De Oliveira ◽  
Christopher Langdon
Keyword(s):  
Symmetric Differentials

Symmetric differentials and variations of Hodge structures

2018 ◽  
Vol 2018 (743) ◽  
pp. 133-161 ◽  
Author(s):  
Yohan Brunebarbe
Keyword(s):  
Cotangent Bundle ◽  
Symmetric Power ◽  
Hodge Structures ◽  
Normal Crossing ◽  
Complex Projective Variety ◽  
Symmetric Differentials ◽  
Variation Of Hodge Structures ◽  
Complex Variation ◽  
Complex Projective ◽  
Simple Normal Crossing

Abstract Let D be a simple normal crossing divisor in a smooth complex projective variety X. We show that the existence on X-D of a non-trivial polarized complex variation of Hodge structures with integral monodromy implies that the pair (X,D) has a non-zero logarithmic symmetric differential (a section of a symmetric power of the logarithmic cotangent bundle). When the corresponding period map is generically immersive, we show more precisely that the logarithmic cotangent bundle is big.

scholarly journals Symmetric Differentials of Rank 1 and Holomorphic Maps

2011 ◽  
Vol 7 (4) ◽  
pp. 1085-1104 ◽  
Author(s):  
Fedor Bogomolov ◽  
Bruno de Oliveira
Keyword(s):  
Holomorphic Maps ◽  
Symmetric Differentials

scholarly journals Symmetric differentials and the fundamental group

2013 ◽  
Vol 162 (14) ◽  
pp. 2797-2813 ◽  
Author(s):  
Yohan Brunebarbe ◽  
Bruno Klingler ◽  
Burt Totaro
Keyword(s):  
Fundamental Group ◽  
Symmetric Differentials
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