Karin Schaller
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View article: LDP Polygons and the Number 12 Revisited
LDP Polygons and the Number 12 Revisited Open
We give a combinatorial proof of a lattice point identity involving a lattice polygon and its dual, generalizing the formula $\operatorname{area}\left(\Delta \right) + \operatorname{area}\left(\Delta^* \right) = 6$ for reflexive $\Delta$. …
View article: On the finite generation of valuation semigroups on toric surfaces
On the finite generation of valuation semigroups on toric surfaces Open
We provide a combinatorial criterion for the finite generation of a valuation semigroup associated with an ample divisor on a smooth toric surface and a non-toric valuation of maximal rank. As an application, we construct a lattice polytop…
View article: LDP polygons and the number 12 revisited
LDP polygons and the number 12 revisited Open
We give a combinatorial proof of a lattice point identity involving a lattice polygon and its dual, generalizing the formula $area(Δ) + area(Δ^*) = 6$ for reflexive $Δ$. The identity is equivalent to the stringy Libgober-Wood identity for …
View article: On the finite generation of valuation semigroups on toric surfaces
On the finite generation of valuation semigroups on toric surfaces Open
We provide a combinatorial criterion for the finite generation of a valuation semigroup associated with an ample divisor on a smooth toric surface and a non-toric valuation of maximal rank. As an application, we construct a lattice polytop…
View article: On the Fine Interior of Three-Dimensional Canonical Fano Polytopes
On the Fine Interior of Three-Dimensional Canonical Fano Polytopes Open
View article: Mirror symmetry for quasi-smooth Calabi–Yau hypersurfaces in weighted projective spaces
Mirror symmetry for quasi-smooth Calabi–Yau hypersurfaces in weighted projective spaces Open
View article: On the Fine Interior of Three-dimensional Canonical Fano Polytopes
On the Fine Interior of Three-dimensional Canonical Fano Polytopes Open
The Fine interior $Δ^{\text{FI}}$ of a $d$-dimensional lattice polytope $Δ$ is a rational subpolytope of $Δ$ which is important for constructing minimal birational models of non-degenerate hypersurfaces defined by Laurent polynomials with …
View article: Stringy Invariants of Algebraic Varieties and Lattice Polytopes
Stringy Invariants of Algebraic Varieties and Lattice Polytopes Open
We present topological invariants in the singular setting for projective ℚ-Gorenstein varieties with at worst log-terminal singularities, such as stringy Euler numbers, stringy Chern classes, stringy Hodge numbers, and stringy E-functions.…
View article: Stringy -functions of canonical toric Fano threefolds and their applications
Stringy -functions of canonical toric Fano threefolds and their applications Open
Let be a -dimensional lattice polytope containing exactly one interior lattice point. We give a simple combinatorial formula for computing the stringy -function of the -dimensional canonical toric Fano variety associated with . Using the s…
View article: Stringy Chern classes of singular toric varieties and their applications
Stringy Chern classes of singular toric varieties and their applications Open
Let X be a normal projective Q-Gorenstein variety with at worst log-terminal singularities. We prove a formula expressing the total stringy Chern class of a generic complete intersection in X via the total stringy Chern class of X. This fo…