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Period Mappings and Period Domains (Cambridge Studies in Advanced Mathematics, Series Number 85)

Period Mappings and Period Domains (Cambridge Studies in Advanced Mathematics)

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51,999 ratings · 2,151 reviews
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OFFICIAL VERIFIED

Period Mappings and Period Domains (Cambridge Studies in Advanced Mathematics, Series Number 85)

Period Mappings and Period Domains (Cambridge Studies in Advanced Mathematics)

4.00 51,999 ratings · 2,151 reviews
Discover Period Mappings and Period Domains (Cambridge Studies in Advanced Mathematics, Series Number 85) by James Carlson. Start reading today and explore ideas, insights, and experiences that stay with you.

Overview: The concept of a period of an elliptic integral goes back to the 18th century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass and others made a systematic study of these integrals. Rephrased in modern terminology, these give a way to encode how the complex structure of a two-torus varies, thereby showing that certain families contain all elliptic curves. Generalizing to higher dimensions resulted in the formulation of the celebrated Hodge conjecture, and in an attempt to solve this, Griffiths generalized the classical notion of period matrix and introduced period maps and period domains which reflect how the complex structure for higher dimensional varieties varies. The basic theory as developed by Griffiths is explained in the first part of the book. Then, in the second part spectral sequences and Koszul complexes are introduced and are used to derive results about cycles on higher dimensional algebraic varieties such as the Noether-Lefschetz theorem and Nori's theorem. Finally, in the third part differential geometric methods are explained leading up to proofs of Arakelov-type theorems, the theorem of the fixed part, the rigidity theorem, and more. Higgs bundles and relations to harmonic maps are discussed, and this leads to striking results such as the fact that compact quotients of certain period domains can never admit a Kahler metric or that certain lattices in classical Lie groups can't occur as the fundamental group of a Kahler manifold.

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Details & Genres

Hodge Theory Books Math Mathematics Mat Number Theory Mat Lie Theory Mat Arithmetic Geometry Mat Algebraic Geometry
Length N/A pages
Published October 20, 2003
ISBN-13 1510040

More Books By: James Carlson


James Carlson
About the Author James Carlson
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After spending years working in the corporate world, James Carlson finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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Jacob Allen
Jacob Allen May 31, 2024
A solid read. The middle dragged a tiny bit, but the ending totally made up for it. Not bad at all.
Rebecca Jackson
Rebecca Jackson July 22, 2024
I have mixed feelings about this one. Some parts were interesting, while others were a bit of a slog to get through. Might work better for someone else, just wasn't completely for me.
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Joshua Evans
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Glad someone recommended this to me. I got really invested in the main character's journey. Everything just clicked for me. Glad I picked this up.
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Kevin Evans February 27, 2024
Glad someone recommended this to me. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Worth the time and money.
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Rebecca Hall August 29, 2024
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Nicholas Miller January 29, 2024
Glad someone recommended this to me. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Definitely recommend it if you like this genre.
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Such a great read. I got really invested in the main character's journey. Everything just clicked for me. Definitely recommend it if you like this genre.
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Charles Hill September 10, 2025
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Richard Sanchez
Richard Sanchez February 20, 2024
It was just alright. The writing was fine, but I didn't feel very connected to the characters. They felt a bit flat. Just right down the middle.
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Such a great read. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. A solid 5/5 for me.
Kimberly Collins
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A very satisfying read. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Will be looking for more from this author.
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Jessica Hill August 09, 2024
An average read for me. It felt a bit repetitive in the middle. Could have been shorter. Just right down the middle.
Joshua Sanchez
Joshua Sanchez May 04, 2024
Pretty good overall. Writing is good, just wish there was a bit more depth in certain parts. Still kept my attention though. Enjoyable weekend read.
George Hill
George Hill February 21, 2025
It was just alright. It had some good moments, but the overall plot felt a bit disjointed in the second half. It's fine if you have nothing else to read.
Gary Thomas
Gary Thomas May 30, 2024
Such a great read. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Will be looking for more from this author.
Joseph Sanchez
Joseph Sanchez November 20, 2025
Glad someone recommended this to me. The author did a great job wrapping everything up at the end. No weird plot holes left behind. Definitely recommend it if you like this genre.
Rebecca Green
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Susan Young
Susan Young October 18, 2024
Really enjoyed this one. I got really invested in the main character's journey. Everything just clicked for me. Glad I picked this up.
Brian Turner
Brian Turner August 30, 2025
A very satisfying read. I got really invested in the main character's journey. Everything just clicked for me. Would probably read it again at some point.
William Phillips
William Phillips December 30, 2025
Took me a few chapters to get into it, but it was worth it. The middle dragged a tiny bit, but the ending totally made up for it. Enjoyable weekend read.
Jacob Moore
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It was okay. It had some good moments, but the overall plot felt a bit disjointed in the second half. A generous 3 stars.
Deborah Robinson
Deborah Robinson June 23, 2024
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Donna Rodriguez
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I liked it for the most part. It held my attention, even if a few things were a little predictable. Still a good book.
Michelle Roberts
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Glad someone recommended this to me. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Definitely recommend it if you like this genre.
Laura Wilson
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Jacob Young
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Really enjoyed this one. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Will be looking for more from this author.
Mary Scott
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Laura Wilson
Laura Wilson September 22, 2025
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Mark Moore
Mark Moore June 20, 2024
Really enjoyed this one. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Glad I picked this up.
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George Rivera
George Rivera September 04, 2024
Glad someone recommended this to me. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Would probably read it again at some point.
Sharon Hernandez
Sharon Hernandez May 16, 2025
Took me a few chapters to get into it, but it was worth it. Writing is good, just wish there was a bit more depth in certain parts. Still kept my attention though. Not bad at all.
John Clark
John Clark August 28, 2025
Finished it in a couple of days. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Glad I picked this up.
Betty Clark
Betty Clark July 07, 2024
I was pleasantly surprised. I loved how the story unfolded. It kept me guessing without being too confusing. Would probably read it again at some point.
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