{"product_id":"what-determines-an-algebraic-variety-ams-216-9780691246819","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 \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-13300639\"\u003eJános Kollár\u003c\/a\u003e, \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-15659133\"\u003eMax Lieblich\u003c\/a\u003e, \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-13324540\"\u003eMartin Olsson\u003c\/a\u003e\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/25\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 240\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.85lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.10h x 6.10w x 0.60d\u003cbr\u003e\u003cb\u003eISBN13:\u003c\/b\u003e 9780691246819\u003cbr\u003e\u003cb\u003eISBN10:\u003c\/b\u003e 0691246815\u003cbr\u003e\u003cb\u003eBISAC Categories:\u003c\/b\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT012010\"\u003eGeometry | Algebraic\u003c\/a\u003e\u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eJános Kollár\u003c\/b\u003e is professor of mathematics at Princeton University and the author of eight books on algebraic geometry, including \u003ci\u003eLectures on Resolution of Singularities\u003c\/i\u003e (Princeton). \u003cb\u003eMax Lieblich \u003c\/b\u003eis the Craig McKibben and Sarah Merner Endowed Professor of Mathematics at the University of Washington, Seattle. \u003cb\u003eMartin Olsson\u003c\/b\u003e is professor of mathematics at the University of California, Berkeley. \u003cb\u003eWill Sawin\u003c\/b\u003e is assistant professor of mathematics at Columbia University.\u003c\/p\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":44456819753197,"sku":"9780691246819","price":118.75,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0550\/8097\/6621\/products\/img_9b096453-5f13-490c-be3b-c9d7c5371233.jpg?v=1700409239","url":"https:\/\/sureshotbooks.com\/products\/what-determines-an-algebraic-variety-ams-216-9780691246819","provider":"SureShot Books Publishing LLC","version":"1.0","type":"link"}