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Hodge Ideals
 
Mircea Mustaţă University of Michigan, Ann Arbor
Mihnea Popa Northwestern University, Evanston, IL
Hodge Ideals
Softcover ISBN:  978-1-4704-3781-7
Product Code:  MEMO/262/1268
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5509-5
Product Code:  MEMO/262/1268.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3781-7
eBook: ISBN:  978-1-4704-5509-5
Product Code:  MEMO/262/1268.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
Hodge Ideals
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Hodge Ideals
Mircea Mustaţă University of Michigan, Ann Arbor
Mihnea Popa Northwestern University, Evanston, IL
Softcover ISBN:  978-1-4704-3781-7
Product Code:  MEMO/262/1268
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5509-5
Product Code:  MEMO/262/1268.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3781-7
eBook ISBN:  978-1-4704-5509-5
Product Code:  MEMO/262/1268.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2622019; 78 pp
    MSC: Primary 14; 32

    The authors use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal. They analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. Saito’s Hodge filtration and Hodge modules
    • 4. Birational definition of Hodge ideals
    • 5. Basic properties of Hodge ideals
    • 6. Local study of Hodge ideals
    • 7. Vanishing theorems
    • 8. Vanishing on ${\mathbf P}^n$ and abelian varieties,with applications
    • Appendix: Higher direct imagesof forms with log poles
    • References
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2622019; 78 pp
MSC: Primary 14; 32

The authors use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal. They analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. Saito’s Hodge filtration and Hodge modules
  • 4. Birational definition of Hodge ideals
  • 5. Basic properties of Hodge ideals
  • 6. Local study of Hodge ideals
  • 7. Vanishing theorems
  • 8. Vanishing on ${\mathbf P}^n$ and abelian varieties,with applications
  • Appendix: Higher direct imagesof forms with log poles
  • References
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.