Vertex Algebroids over Veronese Rings

Vertex Algebroids I

HILBERT SCHEMES and MAXIMAL BETTI NUMBERS over VERONESE RINGS

We show that Macaulay’s Theorem, Gotzmann’s Persistence Theorem, and Green’s Theorem hold over a Veronese toric ring R. We also prove that the Hilbert scheme over R is connected; this is an analogue of Hartshorne’s theorem that the Hilbert scheme over a polynomial ring is connected. Furthermore, we prove that each lex ideal in R has the greatest Betti numbers among all graded ideals with the sa...

Vertex Algebroids Ii

In this note we determine the obstruction to triviality of the stack of exact vertex algebroids thereby recovering the result of [GMS]. The stack EVAOX of exact vertex OX-algebroids is a torsor under the stack in Picard groupoids ECAOX of exact Courant OX -algebroids. The latter is equivalent to the stack of torsors under ΩX −→Ω . Therefore, ECAOX -torsors are classified by H (X; ΩX −→Ω ). The ...

Twisted modules for vertex algebras associated with vertex algebroids

We continue with [LY] to construct and classify graded simple twisted modules for the N-graded vertex algebras constructed by Gorbounov, Malikov and Schechtman from vertex algebroids. Meanwhile we determine the full automorphism groups of those N-graded vertex algebras in terms of the automorphism groups of the corresponding vertex algebroids.

COTORSION DIMENSIONS OVER GROUP RINGS

Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.