Quartic.pdf (903.86 kB)
Non-rigid quartic 3-folds
journal contribution
posted on 2016-06-20, 13:53 authored by Hamid Abban, Anne-Sophie KaloghirosLet 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.
History
School
- Science
Department
- Mathematical Sciences
Published in
Compositio MathematicaVolume
152Issue
5Pages
955 - 983Citation
AHMADINEZHAD, H. and KALOGHIROS, A-S., 2016. Non-rigid quartic 3-folds. Compositio Mathematica, 152(5), pp. 955-983.Publisher
© The Authors. Published by Cambridge University Press (CUP)Version
- VoR (Version of Record)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/Acceptance date
2015-07-07Publication date
2015-12-22Notes
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/ISSN
0010-437XeISSN
1570-5846Publisher version
Language
- en