502 citations · 1k across the 33 of their papers we have counts for
22 papers · 1 filter
Deformations of Calabi-Yau varieties with isolated log canonical singularities
Robert Friedman, Radu Laza
Recent progress in the deformation theory of Calabi-Yau varieties with canonical singularities has highlighted the key role played by the higher Du Bois and higher rational sin…
Deformations of Calabi-Yau varieties with -liminal singularities
Robert Friedman, Radu Laza
The goal of this paper is to describe certain nonlinear topological obstructions for the existence of first order smoothings of mildly singular Calabi-Yau varieties of dimension at…
The higher Du Bois and higher rational properties for isolated singularities
Robert Friedman, Radu Laza
Higher rational and higher Du Bois singularities have recently been introduced as natural generalizations of the standard definitions of rational and Du Bois singularities. In this…
Higher Du Bois and higher rational singularities
Robert Friedman, Radu Laza
We prove that the higher direct images of the sheaves of relative Kähler differentials are locally free and compatible with arbitrary base change for fla…
Deformations of some local Calabi-Yau manifolds
Robert Friedman, Radu Laza
We study deformations of certain crepant resolutions of isolated rational Gorenstein singularities. After a general discussion of the deformation theory, we specialize to dimension…
Deformations of singular Fano and Calabi-Yau varieties
Robert Friedman, Radu Laza
The goal of this paper is to generalize results concerning the deformation theory of Calabi-Yau and Fano threefolds with isolated hypersurface singularites, due to the first author…
The -lemma for general Clemens manifolds
Robert Friedman
We show that the -lemma holds for the non-Kähler compact complex manifolds of dimension three with trivial canonical bundle constructed by Clemens as deform…
Smoothings and Rational Double Point Adjacencies for Cusp Singularities
Philip Engel, Robert Friedman
A cusp singularity is a surface singularity whose minimal resolution is a cycle of smooth rational curves meeting transversely. Cusp singularities come in naturally dual pairs. Loo…
On the geometry of anticanonical pairs
Robert Friedman
The systematic study of rational surfaces with an anticanonical cycle dates back to a fundamental paper of Looijenga in 1981. Recently, Gross, Hacking and Keel have introdu…
On some Hermitian variations of Hodge structure of Calabi-Yau type with real multiplication
Robert Friedman, Radu Laza
We prove that, for every totally real number field E_0, there exists a weight three variation of Hodge structure of Calabi-Yau type defined over the rational numbers with associate…
On the ample cone of a rational surface with an anticanonical cycle
Robert Friedman
Let be a smooth rational surface and let be a cycle of rational curves on which is an anticanonical divisor, i.e. an element of . Looijenga studied the geometry…
Semi-algebraic horizontal subvarieties of Calabi-Yau type
Robert Friedman, Radu Laza
We study horizontal subvarieties of a Griffiths period domain . If is defined by algebraic equations, and if is also invariant under a large discrete subgrou…
On the Geometry of Principal Homogeneous Spaces
A. J. de Jong, Robert Friedman
Let be a curve defined over an algebraically closed field and let be an elliptic surface with base curve . We investigate the geometry of everywhere locally tri…
Cubic threefolds and abelian varieties of dimension five. II
Sebastian Casalaina-Martin
This paper extends joint work with R. Friedman to show that the closure of the locus of intermediate Jacobians of smooth cubic threefolds, in the moduli space of principally polari…
Cubic threefolds and abelian varieties of dimension five
Sebastian Casalaina-Martin, Robert Friedman
This paper proves the following converse to a theorem of Mumford: Let be a principally polarized abelian variety of dimension five, whose theta divisor has a unique singular po…
Automorphism sheaves, spectral covers, and the Kostant and Steinberg sections
Robert Friedman, John W. Morgan
Kostant constructed a section from the adjoint quotient morphism of a simple Lie algebra to the open set of regular elements, and Steinberg constructed such a section for the adjoi…
Holomorphic Principal Bundles Over Elliptic Curves III: Singular Curves and Fibrations
R. Friedman, J. W. Morgan
Let G be a simple and simply connected complex linear algebraic group. In this paper, we discuss the generalization of the parabolic construction of holomorphic principal G-bundles…
Minuscule representations, invariant polynomials, and spectral covers
Robert Friedman, John W. Morgan
Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the a…
Exceptional groups and del Pezzo surfaces
Robert Friedman, John W. Morgan
Given a del Pezzo surface of degree d between 1 and 6, possibly with rational double points, we construct a "tautological" holomorphic G-bundle over X, where G is a reductive group…
On the converse to a theorem of Atiyah and Bott
Robert Friedman, John W. Morgan
Let G be a complex reductive group and let C be a smooth curve of genus at least one. We prove a converse to a theorem of Atiyah-Bott concerning the stratification of the space of…
Holomorphic Principal Bundles Over Elliptic Curves II: The Parabolic Construction
Robert Friedman, John W. Morgan
This paper continues the study of holomorphic semistable principal G-bundles over an elliptic curve. In this paper, the moduli space of all such bundles is constructed by consideri…
Holomorphic principal bundles over elliptic curves
Robert Friedman, John W. Morgan
In this paper, the first of a series of three, we classify holomorphic principal G-bundles over an elliptic curve, where G is a reductive group. We also study the local and global…