TY - JOUR

T1 - Effective estimates for the degrees of maximal special subvarieties

AU - Daw, Christopher

AU - Javanpeykar, Ariyan

AU - Kühne, Lars

N1 - Funding Information: The first author would like to thank the EPSRC and the Institut des Hautes Etudes Scientifiques for granting him a William Hodge fellowship, during which he first began working on this topic. He would like to thank Gopal Prasad and the University of Michigan for a stimulating visit in 2015. He would like to thank the EPSRC again, as well as Jonathan Pila, for the opportunity to be part of the project Model Theory, Functional Transcendence, and Diophantine Geometry. He would like the University of Reading for its ongoing support. He would like to thank both the second and third authors, and their institutions, for invitations to visit. He was latterly supported by an EPSRC New Investigator Award (EP/S029613/1). The second author gratefully acknowledges support from SFB/Transregio 45. He would also like to thank Manfred Lehn and Kang Zuo for helpful discussions. The third author acknowledges support from the Swiss National Science Foundation through an Ambizione Grant (No. 168055). He also would like to thank Philipp Habegger for discussions and encouragement. The authors would like to collectively thank Stefan Müller-Stach for having originally suggested that they work on this problem, and for many helpful discussions. They also thank the referee for several insightful comments and suggestions. Funding Information: The first author would like to thank the EPSRC and the Institut des Hautes Etudes Scientifiques for granting him a William Hodge fellowship, during which he first began working on this topic. He would like to thank Gopal Prasad and the University of Michigan for a stimulating visit in 2015. He would like to thank the EPSRC again, as well as Jonathan Pila, for the opportunity to be part of the project Model Theory, Functional Transcendence, and Diophantine Geometry. He would like the University of Reading for its ongoing support. He would like to thank both the second and third authors, and their institutions, for invitations to visit. He was latterly supported by an EPSRC New Investigator Award (EP/S029613/1). The second author gratefully acknowledges support from SFB/Transregio 45. He would also like to thank Manfred Lehn and Kang Zuo for helpful discussions. The third author acknowledges support from the Swiss National Science Foundation through an Ambizione Grant (No. 168055). He also would like to thank Philipp Habegger for discussions and encouragement. The authors would like to collectively thank Stefan Müller-Stach for having originally suggested that they work on this problem, and for many helpful discussions. They also thank the referee for several insightful comments and suggestions.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - Let Z be an algebraic subvariety of a Shimura variety. We extend results of the first author to prove an effective upper bound for the degree of a non-facteur maximal special subvariety of Z.

AB - Let Z be an algebraic subvariety of a Shimura variety. We extend results of the first author to prove an effective upper bound for the degree of a non-facteur maximal special subvariety of Z.

KW - André–Oort conjecture

KW - Degrees

KW - Effectivity

KW - Shimura varieties

UR - http://www.scopus.com/inward/record.url?scp=85076313132&partnerID=8YFLogxK

U2 - 10.1007/s00029-019-0528-1

DO - 10.1007/s00029-019-0528-1

M3 - Article

AN - SCOPUS:85076313132

VL - 26

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

SN - 1022-1824

IS - 1

M1 - 2

ER -