{"product_id":"algebraic-geometry-i-schemes-with-examples-and-exercises-9783658307325","title":"Algebraic Geometry I: Schemes: With Examples and Exercises","description":"Algebraic geometry has its origin in the study of systems of polynomial equations f (x, . . ., x )=0, 1 1 n . . . f (x, . . ., x )=0. r 1 n Here the f ? k[X, . . ., X ] are polynomials in n variables with coe?cients in a ?eld k. i 1 n n ThesetofsolutionsisasubsetV(f, . . ., f)ofk . Polynomialequationsareomnipresent 1 r inandoutsidemathematics, andhavebeenstudiedsinceantiquity. Thefocusofalgebraic geometry is studying the geometric structure of their solution sets. n If the polynomials f are linear, then V(f, . . ., f ) is a subvector space of k. Its i 1 r \"size\" is measured by its dimension and it can be described as the kernel of the linear n r map k ? k, x=(x, . . ., x ) ? (f (x), . . ., f (x)). 1 n 1 r For arbitrary polynomials, V(f, . . ., f ) is in general not a subvector space. To study 1 r it, one uses the close connection of geometry and algebra which is a key property of algebraic geometry, and whose ?rst manifestation is the following: If g = g f +. . . g f 1 1 r r is a linear combination of the f (with coe?cients g ? k[T, . . ., T ]), then we have i i 1 n V(f, . . ., f)= V(g, f, . . ., f ). Thus the set of solutions depends only on the ideal 1 r 1 r a? k[T, . . ., T ] generated by the f .\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-13326673\"\u003eUlrich Görtz\u003c\/a\u003e, \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-6078225\"\u003eTorsten Wedhorn\u003c\/a\u003e\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer Spektrum\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/28\/2020\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 626\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 2.20lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.61h x 6.69w x 1.28d\u003cbr\u003e\u003cb\u003eISBN13:\u003c\/b\u003e 9783658307325\u003cbr\u003e\u003cb\u003eISBN10:\u003c\/b\u003e 3658307323\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\u003c\/p\u003e\u003cp\u003eProf. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen\u003cbr\u003e Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt\u003c\/p\u003e","brand":"Springer Spektrum","offers":[{"title":"Default Title","offer_id":44590821703917,"sku":"9783658307325","price":149.98,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0550\/8097\/6621\/products\/img_4e17226e-2339-4a04-9c6c-10038790336f.jpg?v=1702265725","url":"https:\/\/sureshotbooks.com\/es\/products\/algebraic-geometry-i-schemes-with-examples-and-exercises-9783658307325","provider":"SureShot Books Publishing LLC","version":"1.0","type":"link"}