{"product_id":"what-determines-an-algebraic-variety-9780691246819","title":"What Determines an Algebraic Variety?","description":"\u003cp\u003e\u003cb\u003eA pioneering new nonlinear approach to a fundamental question in algebraic geometry\u003c\/b\u003e\u003cbr\u003e\u003cbr\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. \u003ci\u003eWhat Determines an Algebraic Variety? \u003c\/i\u003edevelops 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.\u003cbr\u003e\u003cbr\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":"János Kollár","offers":[{"title":"Default Title","offer_id":42960206266486,"sku":"9780691246819","price":75.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0671\/1374\/6550\/files\/CoreSourceHub_baa0209e-ef21-42fe-8463-74c65449230d.jpg?v=1767796135","url":"https:\/\/ingramacademic.com\/products\/what-determines-an-algebraic-variety-9780691246819","provider":"Ingram Academic \u0026 Professional","version":"1.0","type":"link"}