5 papers · 1 filter
Deformations of fibered Calabi--Yau varieties
Benjamin Bakker, Kristin DeVleming, Stefano Filipazzi +5
Kollár showed that small deformations of elliptically fibered smooth -torsion varieties with remain elliptically fibered. We extend this result to any…
Non-abelian Hodge theory for non-proper varieties and the linear Shafarevich conjecture
Benjamin Bakker
We survey recent advances in non-abelian Hodge theory in the "mixed" setting of non-proper algebraic varieties. We then describe how these tools are used to construct algebraic Sha…
Baily--Borel compactifications of period images and the b-semiampleness conjecture
Benjamin Bakker, Stefano Filipazzi, Mirko Mauri +1
We address two questions related to the semiampleness of line bundles arising from Hodge theory. First, we prove there is a functorial compactification of the image of a period map…
Periods in Families and Derivatives of Period Maps
Ben Bakker, Jonathan Pila, Jacob Tsimerman
Given a smooth proper family , we study the (quasi)-periods of the fibers of as (germs of) functions on . We show that they field they generate has the s…
The linear Shafarevich conjecture for quasiprojective varieties and algebraicity of Shafarevich morphisms
Benjamin Bakker, Yohan Brunebarbe, Jacob Tsimerman
We prove that the universal cover of a normal complex algebraic variety admitting a faithful complex representation of its fundamental group is an analytic Zariski open subset of a…