Gerbes of chiral differential operators. III

Gerbes of chiral differential operators. II

Results of our previous note, "Gerbes of chiral differential operators" (Math. Res. Letters, 7(2000), 55-66), are discussed in the algebraic category.

Formal loops IV: Chiral differential operators

We relate the gerbe of sheaves of chiral differential operators (CDO) on a algebraic variety X, studied by Gorbounov, Malikov and Schechtman, to the determinantal gerbe of the formal loop space LX introduced in our earlier paper. The liens of the two gerbes are related by a version of the symplectic action homomorphism. The determinantal gerbe of LX has a factorization structure in the spirit of Beilinson and Drinfeld. In our identification, sheaves of CDO correspond to factorizing objects of this factorization gerbe.

Gerbes of chiral differential operators

In this note we compute the cohomological obstruction to the existence of certain sheaves of vertex algebras on smooth varieties. These sheaves have been introduced and studied in the previous work by A.Vaintrob and two of the authors. Hopefully our result clarifies to some extent the constructions of the above work.

Formal loops III: Factorizing functions and the Radon transform

To any algebraic variety X and and closed 2-form ωon X, we associate the "symplectic action functional" T(ω) which is a function on the formal loop space LX introduced by the authors in math.AG/0107143. The correspondence ω--> T(ω) can be seen as a version of the Radon transform. We give a characterization of the functions of the form T(ω) in terms of factorizability (infinitesimal analog of additivity in holomorphic pairs of pants) as well as in terms of vertex operator algebras. These results will be used in the subsequent paper which will relate the gerbe of chiral differential operators on…

超椭圆 Prym 对模栈的积分 Chow 环 III

The Integral Chow Rings of the Moduli Stacks of Hyperelliptic Prym Pairs III

本文通过商栈描述和刚性化映射的根 gerbe 判别，完成了超椭圆 Prym 对模栈所有不可约分支积分 Chow 环的计算，仅剩一个奇亏格特殊情形未决。