Two-dimensional Virasoro algebras

TL;DR

This paper classifies central extensions of a dg Lie algebra related to 2D geometry and proves a universal Grothendieck--Riemann--Roch theorem for families of complex surfaces.

Contribution

It provides a classification of central extensions of dg Lie algebras in 2D and establishes a universal form of the Grothendieck--Riemann--Roch theorem for complex surface families.

Findings

Classified central extensions of dg Lie algebra on the punctured formal 2-disk.

Proved a local and universal Grothendieck--Riemann--Roch theorem for 2D complex varieties.

Established foundational results connecting 2D Virasoro algebras to algebraic geometry.

Abstract

We classify central extensions of the dg Lie algebra of derived global sections of the tangent sheaf on the punctured, formal 2-disk. We then prove a local and universal form of the Grothendieck--Rieman--Roch theorem for families of two-dimensional complex varieties.