{"product_id":"what-determines-an-algebraic-variety-j-nos-koll-r-9780691246802","title":"What Determines an Algebraic Variety?: (Ams-216)","description":"\u003cp\u003e\u003cb\u003eA pioneering new nonlinear approach to a fundamental question in algebraic geometry\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003c\/p\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. \u003cp\u003e\u003c\/p\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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e J疣os Koll疵, Max Lieblich, Martin Olsson\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0691246807\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691246802\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/25\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 240\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.10lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.30h x 6.20w x 0.80d","brand":"J疣os Koll疵","offers":[{"title":"Hardcover","offer_id":44080268017919,"sku":"9780691246802","price":165.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_6270da73-aec5-42fd-8945-62c1565664a6.jpg?v=1685485862","url":"https:\/\/www.whiterainbookhouse.com\/products\/what-determines-an-algebraic-variety-j-nos-koll-r-9780691246802","provider":"WR Book House","version":"1.0","type":"link"}