caa a22 4500 606161309 CHVBK 20210128100634.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10468-014-9506-7 doi (NATIONALLICENCE)springer-10.1007/s10468-014-9506-7 Noncommutative Blowups of Elliptic Algebras [Elektronische Daten] [D. Rogalski, S. Sierra, J. Stafford] We develop a ring-theoretic approach for blowing up many noncommutative projective surfaces. Let T be an elliptic algebra (meaning that, for some central element ∈T 1, T/g T is a twisted homogeneous coordinate ring of an elliptic curve E at an infinite order automorphism). Given an effective divisor d on E whose degree is not too big, we construct a blowup T(d) of T at d and show that it is also an elliptic algebra. Consequently it has many good properties: for example, it is strongly noetherian, Auslander-Gorenstein, and has a balanced dualizing complex. We also show that the ideal structure of T(d) is quite rigid. Our results generalise those of the first author in Rogalski (Advances Math. 226, 1433-1473, 2011). In the companion paper Rogalski et al. (2013), we apply our results to classify orders in (a Veronese subalgebra of) a generic cubic or quadratic Sklyanin algebra. Springer Science+Business Media Dordrecht, 2014 Noncommutative projective geometry nationallicence Noncommutative surfaces nationallicence Sklyanin algebras nationallicence Noetherian graded rings nationallicence Noncommutative blowing up nationallicence Rogalski D. Department of Mathematics, UCSD, 92093-0112, La Jolla, CA, USA aut Sierra S. School of Mathematics, University of Edinburgh, EH9 3JZ, Edinburgh, UK aut Stafford J. School of Mathematics, The University of Manchester, M13 9PL, Manchester, UK aut Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 491-529 1386-923X 18:2<491 2015 18 10468 https://doi.org/10.1007/s10468-014-9506-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9506-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rogalski D. Department of Mathematics, UCSD, 92093-0112, La Jolla, CA, USA aut NATIONALLICENCE 700 1- Sierra S. School of Mathematics, University of Edinburgh, EH9 3JZ, Edinburgh, UK aut NATIONALLICENCE 700 1- Stafford J. School of Mathematics, The University of Manchester, M13 9PL, Manchester, UK aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 491-529 1386-923X 18:2<491 2015 18 10468