TY - JOUR
T1 - Cyclic covers that are not stably rational
AU - Colliot-Thélène, J. L.
AU - Pirutka, A. V.
N1 - Publisher Copyright:
© 2016 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.
PY - 2016
Y1 - 2016
N2 - Using methods developed by Kollár, Voisin, ourselves and Totaro, we prove that a cyclic cover of PCn , n ≥ 3, of prime degree p, ramified along a very general hypersurface f(x0, ⋯ , xn) = 0 of degree mp, is not stably rational if m(p-1) ≤ n+1 6 mp. In dimension 3 we recover double covers of PC3 ramified along a very general surface of degree 4 (Voisin) and double covers of PC3 ramified along a very general surface of degree 6 (Beauville). We also find double covers of PC4 ramified along a very general hypersurface of degree 6. This method also enables us to produce examples over a number field.
AB - Using methods developed by Kollár, Voisin, ourselves and Totaro, we prove that a cyclic cover of PCn , n ≥ 3, of prime degree p, ramified along a very general hypersurface f(x0, ⋯ , xn) = 0 of degree mp, is not stably rational if m(p-1) ≤ n+1 6 mp. In dimension 3 we recover double covers of PC3 ramified along a very general surface of degree 4 (Voisin) and double covers of PC3 ramified along a very general surface of degree 6 (Beauville). We also find double covers of PC4 ramified along a very general hypersurface of degree 6. This method also enables us to produce examples over a number field.
KW - Chow group of zero-cycles
KW - Cyclic covers
KW - Stable rationality
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U2 - 10.1070/IM8429
DO - 10.1070/IM8429
M3 - Article
AN - SCOPUS:84987615755
SN - 1064-5632
VL - 80
SP - 665
EP - 677
JO - Izvestiya Mathematics
JF - Izvestiya Mathematics
IS - 4
ER -