6 papers
Cyclic covers via mixed Hodge modules
Scott Hiatt
Suppose we are given an arbitrary line bundle on a complex algebraic variety , not necessarily smooth. For a positive integer , suppose there exists a global se…
Topology and Euler characteristics of tropical varieties
Scott Hiatt, Connor Simpson, Botong Wang +1
We study Euler characteristics of tropical subvarieties of tropical abelian varieties. We prove that every H-regular subvariety, locally modeled on tropicalizations of sufficiently…
Differential forms on varieties with pre--rational singularities
Scott Hiatt
Let be a complex algebraic variety. With -coefficients, the compactly supported cohomology groups and the compactly supported intersectio…
Differential Forms and Hodge Structures on Singular Varieties
Donu Arapura, Scott Hiatt
We compare a couple of notions of differential form on singular complex algebraic varieties, and relate them to the outermost associated graded spaces of the Hodge filtration of or…
Equivariant Hodge modules and rational singularities
Donu Arapura, Scott Hiatt
We define a notion of Hodge modules with rational singularities. A variety has rational singularities in the usual sense, if it is normal and the Hodge module related to intersecti…
Vanishing of Local Cohomology with Applications to Hodge Theory
Scott Hiatt
Let be a polarized variation of Hodge structure on a smooth quasi-projective variety By M. Saito's theory of mixed Hodge modules, the vari…