These notes are based on a series of lectures given at the Tata Institute of Fundamental Research, Mumbai, in 2007, on the theme of Hodge theoretic motives associated to various geometric objects. Starting with the topological setting, the notes go on to Hodge theory and mixed Hodge theory on the cohomology of varieties. Degenerations, limiting mixed Hodge structures and the relation to singularities are addressed next. The original proof of Bittner's theorem on the Grothendieck group of varieties, with some applications, is presented as an appendix to one of the chapters. The situation of relative varieties is addressed next using the machinery of mixed Hodge modules. Chern classes for singular varieties are explained in the motivic setting using Bittner's approach, and their full functorial meaning is made apparent using mixed Hodge modules. An appendix explains the treatment of Hodge characteristic in relation with motivic integration and string theory. Throughout these notes, emphasis is placed on explaining concepts and giving examples.
- ISBN:
- 9788184870121
- 9788184870121
- Category:
- Uncategorized
- Publication Date:
- 15-04-2010
- Publisher:
- Tata Institute of Fundamental Research
- Country of origin:
- India
Click 'Notify Me' to get an email alert when this item becomes available
Great!
Click on Save to My Library / Lists
Click on Save to My Library / Lists
Select the List you'd like to categorise as, or add your own
Here you can mark if you have read this book, reading it or want to read
Awesome! You added your first item into your Library
Great! The fun begins.
Click on My Library / My Lists and I will take you there
Click on My Library / My Lists and I will take you there
Reviews
Be the first to review Motivic Aspects of Hodge Theory.
Share This Book: