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03950aam a2200421 i 4500 001 DF86710A6CB211EE935F82A422ECA4DB 003 SILO 005 20231017010119 008 230104t20232023njua b 001 0 eng 010 $a 2022059411 020 $a 0691246815 020 $a 9780691246819 020 $a 0691246807 020 $a 9780691246802 035 $a (OCoLC)1346294487 040 $a DLC $b eng $e rda $c DLC $d YDX $d OCLCF $d UKMGB $d XII $d IND $d YDX $d QGJ $d NUI $d SILO 042 $a pcc 050 04 $a QA1 $b .A626 no.216 100 1 $a KollaÌr, JaÌnos, $e author. $4 aut 245 10 $a What determines an algebraic variety? / $c JaÌnos KollaÌr, Max Lieblich, Martin Olsson, Will Sawin. 264 1 $a Princeton, New Jersey : $b Princeton University Press, $c 2023. 300 $a viii ; 226 pages : $b illustrations ; $c 24 cm. 490 1 $a Annals of mathematics studies, $x 0066-2313 ; $v number 216 520 $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"--Provided by publisher. 520 $a "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"--Provided by publisher. 504 $a Includes bibliographical references (pages [213]-221) and indexes. 505 00 $t Complements, counterexamples, and conjectures. $t Divisorial structures and definable linear systems -- $t Reconstruction from divisorial structures: infinite fields -- $t Reconstruction from divisorial structures: finite fields -- $t Topological geometry -- $t The set-theoretic complete intersection property -- $t Linkage -- $t Complements, counterexamples, and conjectures. 650 0 $a Algebraic varieties. 650 7 $a Algebraic varieties. $2 fast $0 (OCoLC)fst00804944 776 08 $i Online version: $a KollaÌr, JaÌnos. $t What determines an algebraic variety? $d Princeton : Princeton University Press, 2023 $z 9780691246833 $w (DLC) 2022059412 700 1 $a Lieblich, Max, $d 1978- $e author. $4 aut 700 1 $a Olsson, Martin C., $e author. $4 aut 700 1 $a Sawin, Will, $d 1993- $e author. $4 aut 773 18 $w 990007568870202771 $g no:31858072915626 830 0 $a Annals of mathematics studies ; $v no.216. 941 $a 1 952 $l OVUX522 $d 20231117032054.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=DF86710A6CB211EE935F82A422ECA4DBInitiate Another SILO Locator Search