TY - JOUR
T1 - Birational boundedness of low-dimensional elliptic Calabi–Yau varieties with a section
AU - Di Cerbo, Gabriele
AU - Svaldi, Roberto
N1 - Funding Information:
G.D.C. is partially supported by the Simons Foundation and NSF grant DMS-1702358. Most of this work was completed during several visits of R.S. to Columbia University. He would like to thank Columbia University for the hospitality and the nice working environment. He would also like to thank MIT where he was a graduate student and UCSD where he was a visitor when part of this work was completed. He kindly acknowledges financial support from NSF research grant nos 1200656 and 1265263 and Churchill College, Cambridge. During the final revision of this work he was supported by funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 307119. This journal is ○c Foundation Compositio Mathematica 2021.
Publisher Copyright:
© 2021 The Author(s).
PY - 2021/8
Y1 - 2021/8
N2 - We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi–Yau manifolds Y → X with a rational section, provided that dim(Y) ≤ 5 and Y is not of product type. As a consequence, we obtain that there are finitely many possibilities for the Hodge diamond of such manifolds. The result follows from log birational boundedness of Kawamata log terminal pairs (X, Δ) with KX + Δ numerically trivial and not of product type, in dimension at most four.
AB - We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi–Yau manifolds Y → X with a rational section, provided that dim(Y) ≤ 5 and Y is not of product type. As a consequence, we obtain that there are finitely many possibilities for the Hodge diamond of such manifolds. The result follows from log birational boundedness of Kawamata log terminal pairs (X, Δ) with KX + Δ numerically trivial and not of product type, in dimension at most four.
KW - Boundedness of algebraic varieties
KW - Calabi–Yau varieties
KW - Elliptic fibrations
KW - Log Calabi–Yau pairs
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U2 - 10.1112/S0010437X2100717X
DO - 10.1112/S0010437X2100717X
M3 - Article
AN - SCOPUS:85114229890
SN - 0010-437X
VL - 157
SP - 1766
EP - 1806
JO - Compositio Mathematica
JF - Compositio Mathematica
IS - 8
ER -