256 citations · 684 across the 40 of their papers we have counts for
9 papers · 1 filter
Fermat Surface and Group Theory in Symmetry of Rapidity Family in Chiral Potts Model
Shi-shyr Roan
The present paper discusses various mathematical aspects about the rapidity symmetry in chiral Potts model (CPM) in the context of algebraic geometry and group theory . We re-analy…
Toric Representation and Positive Cone of Picard Group and Deformation Space in Mirror Symmetry of Calabi-Yau Hypersurfaces in Toric Varieties
Shi-shyr Roan
We derive the combinatorial representations of Picard group and deformation space of anti-canonical hypersurfaces of a toric variety using techniques in toric geometry. The mirror…
Picard Groups of Hypersurfaces in Toric Varieties
Shi-shyr Roan
We study the structure of rational Picard groups of hypersurfaces of toric varieties. By using the fan structure associated to the ambient toric variety, an explicit basis of the P…
Intermediate Jacobian and Some Arithmetic Properties of Kummer-surface-type CY 3-folds
Shi-shyr Roan
In this article, we examine the arithmetic aspect of the Kummer-surface-type CY 3-folds , characterized by the crepant resolution of 3-torus-orbifold with only iso…
On Branching Indices of Affine A-D-E Diagrams : A Geometrical Characterization by Kleinian Singularities
Shi-shyr Roan
The exceptional configuration of the minimal resolution of a Kleinian quotient surface $S_G (:= \CZ^2/G)$ is depicted by a -- Coxeter-Dynkin diagram. In this…
Rational Curves in Rigid Calabi-Yau Three-folds
Shi-shyr Roan
We determine all the Kummer-surface-type Calabi-Yau (CY) 3-folds, i.e., those which are resolutions of 3-torus-orbifolds with only isolated singularities. There a…
Crepant Resolutions of C^n/A_1(n) and Flops of n-Folds for n = 4,5
Li Chiang, Shi-shyr Roan
In this article, we determine the explicit toric variety structure of $\hl^{A_1(n)}(\CZ^n)$ for , where is the special diagonal group of all order 2 elements. Throu…
On Hypersurface Quotient Singularity of Dimension 4
Li Chiang, Shi-Shyr Roan
We consider geometrical problems on Gorenstein hypersurface orbifolds of dimension through the theory of Hilbert scheme of group orbits. For a linear special group a…
Orbifolds and Finite Group Representations
Li Chiang, Shi-shyr Roan
We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We shall concern only the quotient singularity of…