What determines an algebraic variety?
"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...
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| Główni autorzy: | , , , |
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| Format: | Livre numérique |
| Język: | Anglais |
| Wydane: |
Princeton, New Jersey :
Princeton University Press
2023.
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| Hasła przedmiotowe: | |
| Dostęp online: | Accès Université d'Orléans et IFPM Accès INSA CVL |
| Komentarz: |
Couverture. https://static2.cyberlibris.com/books_upload/136pix/9780691246833.jpg Cyberlibris (ScholarVox) corpus Sciences de l'ingénieur Cyberlibris (ScholarVox) corpus Sciences de l'ingénieur |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • What determines an algebraic variety?, János Kollár, Max Lieblich, Martin Olsson, Will Sawin, 2023, Princeton, New Jersey, Princeton University Press, 1 volume (viii-226 pages), Annals of mathematics studies, 978-0-691-24680-2 |
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| 008 | 250428s2023 xxg ||| |||| 00| 0 eng d | ||
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| 020 | |a 9780691246833 | ||
| 041 | 0 | |a eng | |
| 082 | |a 516.3/53 | ||
| 100 | 1 | |a Kollár, János, |d 1956-...., |c mathématicien. | |
| 245 | 1 | 0 | |a What determines an algebraic variety? |c János Kollár, Max Lieblich, Martin Olsson, Will Sawin. |
| 260 | |a Princeton, New Jersey : |b Princeton University Press, |c 2023. | ||
| 500 | |a Couverture. https://static2.cyberlibris.com/books_upload/136pix/9780691246833.jpg | ||
| 500 | |a Cyberlibris (ScholarVox) corpus Sciences de l'ingénieur | ||
| 500 | |a Cyberlibris (ScholarVox) corpus Sciences de l'ingénieur | ||
| 504 | |a Bibliogr. p. [213]-221. Index | ||
| 506 | |a L'accès en ligne est réservé aux établissements ou bibliothèques ayant souscrit l'abonnement. Cyberlibris | ||
| 520 | |a "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". "In this monograph, the authors approach a rarely considered question in the field of algebraic geometry: to what extent is an algebraic variety X determined by the underlying Zariski topological space X? Before this work, it was believed that the Zariski topology could give only coarse information about X. Using three reconstruction theorems, the authors prove -- astoundingly -- that the variety X is entirely determined by the Zariski topology when the dimension is at least two. It offers both new techniques, as this question had not been previously studied in depth, and future paths for application and inquiry | ||
| 650 | |a Géométrie algébrique | ||
| 650 | |a Variétés algébriques | ||
| 700 | 1 | |a Olsson, Martin C., |d 19..- |4 aut | |
| 700 | 1 | |a Sawin, Will. |4 aut | |
| 700 | 1 | |a Lieblich, Max, |d 1978- |4 aut | |
| 776 | 0 | |0 271777680 |t What determines an algebraic variety? |f János Kollár, Max Lieblich, Martin Olsson, Will Sawin |d 2023 |c Princeton, New Jersey |n Princeton University Press |p 1 volume (viii-226 pages) |s Annals of mathematics studies |z 978-0-691-24680-2 | |
| 856 | 4 | |5 452349901:873404920 |u https://ezproxy.univ-orleans.fr/login?qurl=https://univ.scholarvox.com/book/88957101 |z Accès Université d'Orléans et IFPM | |
| 856 | 4 | |5 180339901:873597826 |u https://ezproxy.insa-cvl.fr/login?qurl=https://univ.scholarvox.com/book/88957101 |z Accès INSA CVL | |
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