16 citations · 35 across the 8 of their papers we have counts for
9 papers
Shafarevich mappings and period mappings
Mark Green, Phillip Griffiths, Ludmil Katzarkov
We shall show that a smooth, quasi-projective variety has a holomorphically convex universal covering $\wt X$ when (i) is residually nilpotent and (ii) there is an adm…
Completions of period mappings: progress report
Mark L Green, Phillip Griffiths, Colleen Robles
We give an informal, expository account of a project to construct completions of period maps.
Natural line bundles on completions of period mappings
Mark Green, Phillip Griffiths, Colleen Robles
We give conditions under which natural lines bundles associated with completions of period mappings are semi-ample and ample.
The LLV decomposition of hyper-Kaehler cohomology
Mark Green, Yoon-Joo Kim, Radu Laza +1
Looijenga--Lunts and Verbitsky showed that the cohomology of a compact hyper-Kähler manifold admits a natural action by the Lie algebra , generaliz…
Positivity of vector bundles and Hodge theory
Mark Green, Phillip Griffiths
It is well known that positivity properties of the curvature of a vector bundle have implications on the algebro-geometric properties of the bundle, such as numerical positivity, v…
Period mappings and properties of the augmented Hodge line bundle
Mark Green, Phillip Griffiths, Radu Laza +1
Let be the image of a period map. We discuss progress towards a conjectural Hodge theoretic completion , an analogue of the Satake-Baily-Borel compactification in…
Deformation Theory and Limiting Mixed Hodge Structures
Mark Green, Phillip Griffiths
This paper was motivated by the following question: Recall that for a smooth projective variety X whose polarized Hodge structure on H^n(X,Q)_{prim} leads to a period point ...
Extremal degenerations of polarized Hodge structures
Mark Green, Phillip Griffiths, Colleen Robles
We describe a Hodge theoretic approach to the question: In what ways can a smooth projective variety degenerate?
The Eisenbud-Koh-Stillman Conjecture on Linear Syzygies
Mark Green
It is proved, as was conjectured by Eisenbud-Koh-Stillman, that for a finitely generated graded module over the symmetric algebra , if the Koszul group ${\cal K}_{p,0}(M,…