{"product_id":"oscar-zariski-oscar-zariski-9780262519533","title":"Oscar Zariski: Collected Papers, Volume 2: Holomorphic Functions and Linear Systems","description":"This is the second of four volumes that will eventually present the full corpus of Zariski's mathematical contributions. Like the first volume (subtitled \u003ci\u003eFoundations of Algebraic Geometry and Resolution of Singularities\u003c\/i\u003e and edited by H. Hironaka and D. Mumford), it is divided into two parts, each devoted to a large but circumscribed area of research activity.\u003cp\u003eThe first part, containing eight papers introduced by Artin, deals with the theory of formal holomorphic functions on algebraic varieties over fields of any characteristic. The primary concern, in Zariski's words, is \"analytic properties of an algebraic variety \u003ci\u003eV\u003c\/i\u003e, either in the neighborhood of a point (strictly \u003ci\u003elocal\u003c\/i\u003e theory) or - and this is the deeper aspect of the theory - in the neighborhood of an algebraic subvariety of \u003ci\u003eV\u003c\/i\u003e (semiglobal theory).\"\u003c\/p\u003e\u003cp\u003eMumford surveys the ten papers reprinted in the second part. These deal with linear systems and the Riemann-Roch theorem and its applications, again in arbitrary characteristic. The applications are primarily to algebraic surfaces and include minimal models and characterization of rational or ruled surfaces.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Oscar Zariski\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0262519534\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780262519533\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e MIT Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/26\/1979\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 530\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.97lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 10.00h x 6.88w x 1.07d","brand":"Oscar Zariski","offers":[{"title":"Paperback","offer_id":48448786137343,"sku":"9780262519533","price":60.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_e7f4b5d9-3741-49ae-aecb-ca077f8176d0.jpg?v=1777260541","url":"https:\/\/www.whiterainbookhouse.com\/products\/oscar-zariski-oscar-zariski-9780262519533","provider":"WR Book House","version":"1.0","type":"link"}