Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 282-305 |
| Seitenumfang | 24 |
| Fachzeitschrift | Journal of the London Mathematical Society |
| Jahrgang | 97 |
| Ausgabenummer | 2 |
| Publikationsstatus | Veröffentlicht - 6 Apr. 2018 |
Abstract
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in: Journal of the London Mathematical Society, Jahrgang 97, Nr. 2, 06.04.2018, S. 282-305.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Automorphisms of minimal entropy on supersingular K3 surfaces
AU - Brandhorst, Simon
AU - González-Alonso, Víctor
N1 - Funding information: The financial support of the starting grant ERC StG 279723 ‘Arithmetic of Algebraic Surfaces’ (SURFARI), the research training group DFG GRK 1463 ‘Analysis, Geometry and String Theory’ and the project MTM2015-69135-P of the spanish ‘Ministerio de Economía y Competitividad’ is gratefully acknowledged.
PY - 2018/4/6
Y1 - 2018/4/6
N2 - In this article we give a strategy to decide whether the logarithm of a given Salem number is realized as entropy of an automorphism of a supersingular K3 surface in positive characteristic. As test case it is proved that log λd, where λd is the minimal Salem number of degree d, is realized in characteristic 5 if and only if d ≤ 22 is even and d ≠ 18. In the complex projective setting we settle the case of entropy log λ12, left open by McMullen, by giving the construction. A necessary and sufficient test is developed to decide whether a given isometry of a hyperbolic lattice, with spectral radius bigger than one, is positive, that is, preserves a chamber of the positive cone.
AB - In this article we give a strategy to decide whether the logarithm of a given Salem number is realized as entropy of an automorphism of a supersingular K3 surface in positive characteristic. As test case it is proved that log λd, where λd is the minimal Salem number of degree d, is realized in characteristic 5 if and only if d ≤ 22 is even and d ≠ 18. In the complex projective setting we settle the case of entropy log λ12, left open by McMullen, by giving the construction. A necessary and sufficient test is developed to decide whether a given isometry of a hyperbolic lattice, with spectral radius bigger than one, is positive, that is, preserves a chamber of the positive cone.
UR - http://www.scopus.com/inward/record.url?scp=85042137343&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1609.02716
DO - 10.48550/arXiv.1609.02716
M3 - Article
AN - SCOPUS:85042137343
VL - 97
SP - 282
EP - 305
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
SN - 0024-6107
IS - 2
ER -