Gorenstein simplices with the given h*-polynomial are classified up to unimodular equivalence by strict divisor chains in the divisor lattice of v, yielding an explicit counting formula.
Gorenstein Simplices and Even Binary Self-Complementary Codes
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
It is known that if a Gorenstein simplex of dimension \(d\) and degree \(s\) is not a lattice pyramid, then \(d \leq 2s-1\). In this paper, we study the extremal case \(d=2s-1\). More precisely, we characterize Gorenstein simplices of dimension \(2s-1\) and degree \(s\) which are not lattice pyramids in terms of even binary self-complementary codes. As an application, combining this characterization with existing classification results on reflexive simplices, we classify Gorenstein simplices of degree \(3\) and \(4\). Equivalently, we classify polarized \(d\)-dimensional Gorenstein fake weighted projective spaces \((X,L)\) satisfying $-K_X=(d-2)L$ or $-K_X=(d-3)L$, where \(-K_X\) is the anticanonical divisor of \(X\) and \(L\) is a Cartier divisor on \(X\).
fields
math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Classification and counting of Gorenstein simplices with $h^*$-polynomial $1+t^k+\cdots+t^{(v-1)k}$
Gorenstein simplices with the given h*-polynomial are classified up to unimodular equivalence by strict divisor chains in the divisor lattice of v, yielding an explicit counting formula.