Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Algebraic Varieties: Minimal Models and Finite Generation
    Show more authors
    • You may already have access via personal or institutional login
  • Select format
  • Publisher:
    Cambridge University Press
    Publication date:
    June 2024
    June 2024
    ISBN:
    9781009344647
    9781009344678
    DOI:
    https://doi.org/10.1017/9781009344647
    Dimensions:
    (229 x 152 mm)
    Weight & Pages:
    0.539kg, 262 Pages
    Dimensions:
    Weight & Pages:
    • Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    Cambridge Studies in Advanced Mathematics
You may already have access via personal or institutional login
    • Selected: Digital
    Add to cart View cart Buy from Cambridge.org
    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    Cambridge Studies in Advanced Mathematics
    Information

    Book description

    The finite generation theorem is a major achievement in modern algebraic geometry. Based on the minimal model theory, it states that the canonical ring of an algebraic variety defined over a field of characteristic 0 is a finitely generated graded ring. This graduate-level text is the first to explain this proof. It covers the progress on the minimal model theory over the last 30 years, culminating in the landmark paper on finite generation by Birkar‒Cascini‒Hacon‒McKernan. Building up to this proof, the author presents important results and techniques that are now part of the standard toolbox of birational geometry, including Mori's bend-and-break method, vanishing theorems, positivity theorems, and Siu's analysis on multiplier ideal sheaves. Assuming only the basics in algebraic geometry, the text keeps prerequisites to a minimum with self-contained explanations of terminology and theorems.

    Refine List

    Actions for selected content:

    Select all | Deselect all
    • View selected items
    • Export citations
    • Download PDF (zip)
    • Save to Kindle
    • Save to Dropbox
    • Save to Google Drive

    Save Search

    You can save your searches here and later view and run them again in "My saved searches".

    Please provide a title, maximum of 40 characters.
    Cancel
    ×

    Contents

    Contents
    References

    Metrics

    Altmetric attention score

    Full text views

    Total number of HTML views: 0
    Total number of PDF views: 0 *
    Loading metrics...

    Book summary page views

    Total views: 0 *
    Loading metrics...

    * Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

    Usage data cannot currently be displayed.

    Accessibility standard: Unknown

    Why this information is here

    This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

    Accessibility Information

    Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.