{"product_id":"9780691246802-what-determines-an-algebraic-variety","title":"What Determines an Algebraic Variety?","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003e\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\n\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":55808905478518,"sku":"9780691246802","price":138.92,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_28640124.jpg?v=1750443339","url":"https:\/\/www.rarewaves.com\/products\/9780691246802-what-determines-an-algebraic-variety","provider":"Rarewaves.com","version":"1.0","type":"link"}