5 citations · 12 across the 14 of their papers we have counts for
15 papers
Murphy's law in non-abelian Hodge theory
Gregorio Baldi, Yeuk Hay Joshua Lam
We construct explicit examples of non-integral variations of -Hodge structures. Our approach leverages Fenchel--Nielsen-type parameterizations, due to Kabaya and Maskit…
Algebraic Hodge generic points are dense
Gregorio Baldi, Gal Binyamini, David Urbanik
Let be a quasi-projective family of varieties defined over . We show that the points of that are H…
Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group
Gregorio Baldi, Benson Farb, Ariyan Javanpeykar +1
Let be the moduli space of smooth complex cubic surfaces and let be its (orbifold) fundamental group. We prove that the ``divisor subgroup'' of $π_…
Intersections and the Bézout Range: Abelian Varieties
Gregorio Baldi, David Urbanik
Given subvarieties of a complex algebraic variety of complementary dimension, must they intersect? When is projective space, this is a consequence of the classical B…
Rich representations and superrigidity
Gregorio Baldi, Nicholas Miller, Matthew Stover +1
We investigate and compare applications of the Zilber-Pink conjecture and dynamical methods to rigidity problems for arithmetic real and complex hyperbolic lattices. Along the way…
Non-density of the exceptional components of the Noether-Lefschetz locus
Gregorio Baldi, Bruno Klingler, Emmanuel Ullmo
We study when the Picard group of smooth surfaces of degree in acquires extra classes. In particular we show that the so called exceptional components of t…
On the Geometric Zilber-Pink Theorem and the Lawrence-Venkatesh method
Gregorio Baldi, Bruno Klingler, Emmanuel Ullmo
Using our recent results on the algebraicity of the Hodge locus for variations of Hodge structures of level at least , we improve the results of Lawrence-Venkatesh in direction…
On the distribution of the Hodge locus
Gregorio Baldi, Bruno Klingler, Emmanuel Ullmo
Given a polarizable -variation of Hodge structures over a complex smooth quasi-projective base , a classical result of Cattani, Deligne and Kaplan says…
Manin-Mumford in arithmetic pencils
Gregorio Baldi, Rodolphe Richard, Emmanuel Ullmo
We obtain a refinement of Manin-Mumford (Raynaud's Theorem) for abelian schemes over some ring of integers. Torsion points are replaced by special 0-cycles, that is reductions modu…
Special subvarieties of non-arithmetic ball quotients and Hodge Theory
Gregorio Baldi, Emmanuel Ullmo
Let be a lattice, and the associated ball quotient. We prove that, if contains infinitely many maximal totally geodesic subvarieties,…
Some remarks on motivical and derived invariants
Gregorio Baldi
We discuss several conjectures about derived equivalent varieties, defined over fields of arbitrary characteristics, and implications among them. In particular we show that the (co…
Finite descent obstruction for Hilbert modular varieties
Gregorio Baldi, Giada Grossi
Let be a finite set of primes. We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of -points on integral models…
On a conjecture of Buium and Poonen
Gregorio Baldi
Given a correspondence between a modular curve and an elliptic curve , we prove that the intersection of any finite-rank subgroup of with the set of points on corres…
On the geometric Mumford-Tate conjecture for subvarieties of Shimura varieties
Gregorio Baldi
We study the image of -adic representations attached to subvarieties of Shimura varieties that are not contained in a smaller Shimura subvariety and have no isotr…
Local to global principle for the moduli space of K3 surfaces
Gregorio Baldi
Recently S. Patrikis, J.F. Voloch and Y. Zarhin have proven, assuming several well known conjectures, that the finite descent obstruction holds on the moduli space of principally p…