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Certain degenerations of surfaces in fake weighted projective -space
Julius Giesler
We study degenerations (along an edge) of surfaces in (fake) weighted projective -space. We introduce the Hodge theoretic data and show that the Hodge loci of vanishing cycles b…
Jacobian rings and the infinitesimal Torelli Theorem
Julius Giesler
In this article we deal with jacobian rings and identify a mixed Hodge component of a nondegenerate hypersurface in the torus with a lattice geometric quotient vector space. We int…
The Kodaira-Spencer map for minimal toric hypersurfaces
Julius Giesler
In this article we study infinitesimal deformations of toric hypersurfaces. We introduce a Kodaira-Spencer map and compute its kernel. By introducing some new Laurent polynomials w…
The plurigenera of nondegenerate minimal toric hypersurfaces
Julius Giesler
In this article we present a formula for the plurigenera of minimal models of nondegenerate toric hypersurfaces, which is valid in arbitrary dimension and which expresses these inv…
Kanev and Todorov surfaces in toric 3-folds
Julius Giesler
In the first part of this article we show for some examples of surfaces of general type in toric 3-folds how to construct minimal and canonical models by toric methods explicitly.…