{"product_id":"9780691246819","title":"What Determines an Algebraic Variety? (Annals of Mathematics Studies)","description":"\u003cp\u003eA pioneering new nonlinear approach to a fundamental question in algebraic geometry\u003c\/p\u003e\n\n\u003cp\u003eOne 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.\u003c\/p\u003e\n\n\u003cp\u003eStarting 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.\u003c\/p\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":42717855809611,"sku":"00000_00000_00000_00000","price":2816.61,"currency_code":"THB","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0641\/0023\/7387\/files\/9780691246819-1.jpg?v=1783351985","url":"https:\/\/kinokuniya.co.th\/th\/products\/9780691246819","provider":"Books Kinokuniya Thailand","version":"1.0","type":"link"}