{"product_id":"what-determines-an-algebraic-variety-book-martin-olsson-9780691246819","title":"What Determines an Algebraic Variety?","description":"A pioneering new nonlinear approach to a fundamental question in algebraic geometry  One of the crowning achievements of nineteenth-century mathematics was the proof that the geometry of lines in space uniquely determines the Cartesian coordinates, up to a linear ambiguity. What Determines an Algebraic Variety? develops a nonlinear version of this theory, offering the first nonlinear generalization of the seminal work of Veblen and Young in a century. While the book uses cutting-edge techniques, the statements of its theorems would have been understandable a century ago; despite this, the results are totally unexpected. Putting geometry first in algebraic geometry, the book provides a new perspective on a classical theorem of fundamental importance to a wide range of fields in mathematics.  Starting with basic observations, the book shows how to read off various properties of a variety from its geometry. The results get stronger as the dimension increases. The main result then says that a normal projective variety of dimension at least 4 over a field of characteristic 0 is completely determined by its Zariski topological space. There are many open questions in dimensions 2 and 3, and in positive characteristic.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49749792063761,"sku":"NGR9780691246819","price":74.19,"currency_code":"USD","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51005765419281,"sku":"NIN9780691246819","price":75.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0691246815.jpg?v=1751199820","url":"https:\/\/www.worldofbooks.com\/products\/what-determines-an-algebraic-variety-book-martin-olsson-9780691246819","provider":"World of Books ","version":"1.0","type":"link"}