{"title":"János Kollár","description":null,"products":[{"product_id":"what-determines-an-algebraic-variety-book-martin-olsson-9780691246819","title":"What Determines an Algebraic Variety?","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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49749792063761,"sku":"NGR9780691246819","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51005765419281,"sku":"NIN9780691246819","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0691246815.jpg?v=1751199820"},{"product_id":"rational-and-nearly-rational-varieties-book-alessio-corti-9780521832076","title":"Rational and Nearly Rational Varieties","description":"Arising from a summer school course taught by J nos Koll r, this book develops the modern theory of rational varieties at a level appropriate for graduate study. Koll r's original course has been developed, with his co-authors, into a state-of-the-art treatment of the classification of algebraic varieties. The authors have included numerous exercises with solutions, which help students reach the stage where they can begin to tackle related contemporary research problems.","brand":"WoB","offers":[{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50338738274577,"sku":"CIN0521533740VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":50356109607185,"sku":"CIN0521533740G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52588539642129,"sku":"NLS9780521832076","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52735473647889,"sku":"NIN9780521832076","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0521533740.jpg?v=1750943477"},{"product_id":"families-of-varieties-of-general-type-book-jnos-kollr-9781009346108","title":"Families of Varieties of General Type","description":"This book gives the first complete treatment of the moduli theory of varieties of dimension larger than one, aimed at researchers and graduate students in algebraic geometry and related areas. The first chapter provides a historical introduction to the subject, while later chapters provide all necessary background material.","brand":"WoB","offers":[{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50377578086673,"sku":"CIN1009346105VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51012322492689,"sku":"NIN9781009346108","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1009346105.jpg?v=1751236141"},{"product_id":"singularities-of-the-minimal-model-program-book-jnos-kollr-9781107035348","title":"Singularities of the Minimal Model Program","description":"This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51019445829905,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51019448156433,"sku":"NIN9781107035348","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1107035341.jpg?v=1751048598"}],"url":"https:\/\/www.worldofbooks.com\/de-de\/collections\/autor-buecher-von-jnos-kollr.oembed","provider":"World of Books ","version":"1.0","type":"link"}