Domingo Toledo

Publications : 74
Aldex : 20
H-index : 15
Citations : 809

Hassler Whitney collected papers

Hassler Whitney et 3 al.

Jan 1, 1992
We present here the mathematical papers of Hassler Whitney. This collection contains all the published papers, with the exception of some short announcements that Whimey did not wish to be included. We also include the introduction to his book Geometric Integration Theory, and one previously unpublished manuscript on the four-color problem. The papers are presented under some broad categories: gra...

Residual finiteness for central extensions of lattices in $\mathrm{PU}(n,1)$ and negatively curved projective varieties

Matthew Stover, Domingo Toledo

Aug 27, 2021 in Arxiv
We study residual finiteness for cyclic central extensions of cocompact arithmetic lattices $\Gamma < \mathrm{PU}(n,1)$ simple type. We prove that the preimage of $\Gamma$ in any connected cover of $\mathrm{PU}(n,1)$, in particular the universal cover, is residually finite. This follows from a more general theorem on residual finiteness of extensions whose characteristic class is contained in the ...

Bounded negativity of self-intersection numbers of Shimura curves on Shimura surfaces

Martin Moeller, Domingo Toledo

Jul 19, 2014 in Arxiv
Shimura curves on Shimura surfaces have been a candidate for counterexamples to the bounded negativity conjecture. We prove that they do not serve this purpose: there are only finitely many whose self-intersection number lies below a given bound. Previously, this result has been shown in [BHK+13] for compact Hilbert modular surfaces using the Bogomolov-Miyaoka-Yau inequality. Our approach uses equ...

Residually finite lattices in $\widetilde{\mathrm{PU}(2,1)}$ and fundamental groups of smooth projective surfaces

Matthew Stover, Domingo Toledo

May 26, 2021 in Arxiv
This paper studies residual finiteness of lattices in the universal cover of $\mathrm{PU}(2,1)$ and applications to the existence of smooth projective varieties with fundamental group a cocompact lattice in $\mathrm{PU}(2,1)$ or a finite covering of it. First, we prove that certain lattices in the universal cover of $\mathrm{PU}(2,1)$ are residually finite. To our knowledge, these are the first su...

A Complex Hyperbolic Structure for Moduli of Cubic Surfaces

Daniel Allcock et 3 al.

Sep 12, 1997 in Arxiv
We show that the moduli space M of marked cubic surfaces is biholomorphic to the quotient by a discrete group generated by complex reflections of the complex four-ball minus the reflection hyperplanes of the group. Thus M carries a complex hyperbolic structure: an (incomplete) metric of constant holomorphic sectional curvature.

Arakelov-Milnor inequalities and maximal variations of Hodge structure

Olivier Biquard et 4 al.

Jan 7, 2021 in Arxiv
In this paper we study the $\mathbb{C}^*$-fixed points in moduli spaces of Higgs bundles over a compact Riemann surface for a complex semisimple Lie group and its real forms. These fixed points are called Hodge bundles and correspond to complex variations of Hodge structure. We introduce a topological invariant for Hodge bundles that generalizes the Toledo invariant appearing for Hermitian Lie gro...

Geometric Integration Theory

James Eells, Domingo Toledo

Jan 1, 1992


Daniel Allcock et 3 al.

Jan 1, 2001
The purpose of this note is to study the geometry of certain remarkable infinite arrangements of hyperplanes in complex hyperbolic space which we call orthogonal arrangements: whenever two hyperplanes meet, they meet at right angles. A natural example of such an arrangement appears in [3]; see also [2]. The concrete theorem that we prove here is that the fundamental group of the complement of an o...


Variations of Hodge structure of maximal dimension

James A. Carlson et 3 al.

Jan 1, 1989 in Duke Mathematical Journal

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