# String Cohomology of a Toroidal Singularity

@article{Borisov1998StringCO, title={String Cohomology of a Toroidal Singularity}, author={Lev Borisov}, journal={arXiv: Algebraic Geometry}, year={1998} }

We construct explicitly regular sequences in the semigroup ring $R=\CC[K]$ of lattice points of the graded cone $K$. We conjecture that the quotients of $R$ by these sequences describe locally string-theoretic cohomology of a toroidal singularity associated to $K$. As a byproduct, we give an elementary proof of the result of Hochster that semigroup rings of rational polyhedral cones are Cohen-Macaulay.

## 12 Citations

All toric l.c.i.-singularities admit projective crepant resolutions

- Mathematics
- 1998

It is known that the underlying spaces of all abelian quotient singularities which are embeddable as complete intersections of hypersurfaces in an affine space can be overall resolved by means of…

The orbifold Chow ring of toric Deligne-Mumford stacks

- Mathematics
- 2004

Generalizing toric varieties, we introduce toric Deligne-Mumford stacks which correspond to combinatorial data. The main result in this paper is an explicit calculation of the orbifold Chow ring of a…

Chiral rings of vertex algebras of mirror symmetry

- Mathematics
- 2002

Abstract.We calculate chiral rings of the N=2 vertex algebras constructed from the combinatorial data of toric mirror symmetry and show that they coincide with the description of stringy cohomology…

Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system

- Mathematics
- 2012

We generalize the combinatorial description of the orbifold (Chen--Ruan) cohomology and of the Grothendieck ring of a Deligne--Mumford toric stack and its associated stacky fan in a lattice $N$ in…

Stringy $E$-functions of Pfaffian�Grassmannian double mirrors

- MathematicsAlgebraic Geometry
- 2019

We establish the equality of stringy $E$-functions for double mirror Calabi-Yau complete intersections in the varieties of skew forms of rank at most $2k$ and at most $n-1-2k$ on a vector space of…

Applications of homological mirror symmetry to hypergeometric systems: duality conjectures

- Mathematics
- 2013

Vertex Algebras and Mirror Symmetry

- Mathematics
- 2001

Abstract: Mirror Symmetry for Calabi–Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to…

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