Heights and periods of algebraic cycles in families
We consider the Beilinson-Bloch heights and Abel-Jacobian periods of homologically trivial
Chow cycles in families. For the Beilinson-Bloch heights, we show that for any $ g\ge 3$, we …
Chow cycles in families. For the Beilinson-Bloch heights, we show that for any $ g\ge 3$, we …
On the torsion locus of the Ceresa normal function
M Kerr, S Tayou - arxiv preprint arxiv:2406.19366, 2024 - arxiv.org
We prove that the positive-dimensional part of the torsion locus of the Ceresa normal
function in $\mathcal {M} _g $ is not Zariski dense when $ g\geq 3$. Moreover, it has only …
function in $\mathcal {M} _g $ is not Zariski dense when $ g\geq 3$. Moreover, it has only …
Special subvarieties of non-arithmetic ball quotients and Hodge Theory
G Baldi, E Ullmo - Annals of Mathematics, 2023 - projecteuclid.org
Abstract Let Γ⊂PU(1,n) be a lattice and S_Γ be the associated ball quotient. We prove that,
if S_Γ contains infinitely many maximal complex totally geodesic subvarieties, then Γ is …
if S_Γ contains infinitely many maximal complex totally geodesic subvarieties, then Γ is …
Sets of special subvarieties of bounded degree
D Urbanik - Compositio Mathematica, 2023 - cambridge.org
Sets of special subvarieties of bounded degree Page 1 Sets of special subvarieties of
bounded degree David Urbanik Compositio Math. 159 (2023), 616–657. doi:10.1112/S0010437X23007029 …
bounded degree David Urbanik Compositio Math. 159 (2023), 616–657. doi:10.1112/S0010437X23007029 …
Geometric G-functions and atypicality
D Urbanik - arxiv preprint arxiv:2301.01857, 2023 - arxiv.org
We describe a general method for giving $ p $-adic interpretations of $ G $-functions arising
from degenerating periods of smooth projective algebraic varieties. Using this, we are able …
from degenerating periods of smooth projective algebraic varieties. Using this, we are able …
On the geometric Zilber–Pink theorem and the Lawrence–Venkatesh method
G Baldi, B Klingler, E Ullmo - Expositiones Mathematicae, 2023 - Elsevier
On the Geometric Zilber–Pink theorem and the Lawrence–Venkatesh method -
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …
Hodge theory, between algebraicity and transcendence
B Klingler - Proc. Int. Cong. Math, 2022 - ems.press
The Hodge theory of complex algebraic varieties is at heart a transcendental comparison of
two algebraic structures. We survey the recent advances bounding this transcendence …
two algebraic structures. We survey the recent advances bounding this transcendence …
Absolutely special subvarieties and absolute Hodge cycles
T Kreutz - arxiv preprint arxiv:2111.00216, 2021 - arxiv.org
We introduce the notion of dR-absolutely special subvarieties in motivic variations of Hodge
structure as special subvarieties cut out by (de Rham-) absolute Hodge cycles and …
structure as special subvarieties cut out by (de Rham-) absolute Hodge cycles and …
Degrees of Hodge Loci
D Urbanik - arxiv preprint arxiv:2412.08924, 2024 - arxiv.org
We prove asymptotic estimates for the growth in the degree of the Hodge locus in terms of
arithmetic properties of the integral vectors that define it. Our methods are general and apply …
arithmetic properties of the integral vectors that define it. Our methods are general and apply …
Arithmetic Deformation of Line Bundles
D Urbanik, Z Yang - arxiv preprint arxiv:2310.08652, 2023 - arxiv.org
We introduce a new method to study mixed characteristic deformation of line bundles. In
particular, for sufficiently large smooth projective families $ f:\mathcal {X}\to\mathcal {S} …
particular, for sufficiently large smooth projective families $ f:\mathcal {X}\to\mathcal {S} …