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Title: Non-rigid quartic 3-folds
Authors: Ahmadinezhad, Hamid
Kaloghiros, Anne-Sophie
Issue Date: 2016
Publisher: © The Authors. Published by Cambridge University Press (CUP)
Citation: AHMADINEZHAD, H. and KALOGHIROS, A-S., 2016. Non-rigid quartic 3-folds. Compositio Mathematica, 152(5), pp. 955-983.
Abstract: Let X⊂P4 be a terminal factorial quartic 3-fold. If X is non-singular, X is birationally rigid, i.e. the classical minimal model program on any terminal Q-factorial projective variety Z birational to X always terminates with X. This no longer holds when X is singular, but very few examples of non-rigid factorial quartics are known. In this article, we first bound the local analytic type of singularities that may occur on a terminal factorial quartic hypersurface X⊂P4. A singular point on such a hypersurface is of type cAn (n ≥ 1), or of type cDm (m ≥ 4) or of type cE6, cE7 or cE8. We first show that if (P 2 X) is of type cAn, n is at most 7 and, if (PϵX) is of type cDm, m is at most 8. We then construct examples of non-rigid factorial quartic hypersurfaces whose singular loci consist (a) of a single point of type cAn for 2≤n≤7, (b) of a single point of type cDm for m = 4 or 5 and (c) of a single point of type cEk for k = 6, 7 or 8.
Description: This is an Open Access Article. It is published by Cambridge University Press under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/
Version: Published
DOI: 10.1112/S0010437X15007769
URI: https://dspace.lboro.ac.uk/2134/21726
Publisher Link: http://dx.doi.org/10.1112/S0010437X15007769
ISSN: 0010-437X
Appears in Collections:Published Articles (Maths)

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