{"product_id":"9780691246802","title":"What Determines An Algebraic Variety?: (Ams-216) (Annals Of Mathematics Studies, 216)","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.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003e| \u003cb\u003eAuthor: \u003c\/b\u003eJános Kollár|Max Lieblich|Martin Olsson|Will Sawin\u003c\/li\u003e\n\u003cli\u003e| \u003cb\u003ePublisher: \u003c\/b\u003ePrinceton University Press\u003c\/li\u003e\n\u003cli\u003e| \u003cb\u003ePublication Date: \u003c\/b\u003eJul 25, 2023\u003c\/li\u003e\n\u003cli\u003e| \u003cb\u003eNumber of Pages: \u003c\/b\u003e240 pages\u003c\/li\u003e\n\u003cli\u003e| \u003cb\u003eLanguage: \u003c\/b\u003eEnglish\u003c\/li\u003e\n\u003cli\u003e| \u003cb\u003eBinding: \u003c\/b\u003eHardcover\u003c\/li\u003e\n\u003cli\u003e| \u003cb\u003eISBN-10: \u003c\/b\u003e0691246807\u003c\/li\u003e\n\u003cli\u003e| \u003cb\u003eISBN-13: \u003c\/b\u003e9780691246802\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48933183160625,"sku":"9780691246802","price":205.29,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0798\/8215\/8385\/files\/9780691246802.jpg?v=1713696371","url":"https:\/\/www.recomparo.com\/products\/9780691246802","provider":"ReComparo.com","version":"1.0","type":"link"}