Algebraic Structures in Extended Geometry

Extended Powers and Steenrod Operations in Algebraic Geometry

Steenrod operations were defined by Voedvodsky in motivic cohomology in order to prove the Milnor and Bloch-Kato conjectures. These operations have also been constructed by Brosnan for Chow rings [5]. The purpose of this paper is to provide a setting for the construction of the Steenrod operations in algebraic geometry, for generalized cohomology theories whose formal group law has order two. W...

Algebraic Structures and Differential Geometry in 2d String Theory

A careful treatment of closed string BRST cohomology shows that there are more discrete states and associated symmetries in D = 2 string theory than has been recognized hitherto. The full structure, at the SU(2) radius, has a natural description in terms of abelian gauge theory on a certain three dimensional cone Q. We describe precisely how symmetry currents are constructed from the discrete s...

Introductory Geometry: Algebraic Geometry

Moduli of Curves and Spin Structures via Algebraic Geometry

Here we investigate some birational properties of two collections of moduli spaces, namely moduli spaces of (pointed) stable curves and of (pointed) spin curves. In particular, we focus on vanishings of Hodge numbers of type (p, 0) and on computations of the Kodaira dimension. Our methods are purely algebro-geometric and rely on an induction argument on the number of marked points and the genus...

Algebraic Geometry

Physical objects and constraints may be modeled by polynomial equations and inequalities. For this reason algebraic geometry, the study of solutions to systems of polynomial equations, is a tool for scientists and engineers. Moreover, relations between concepts arising in science and engineering are often described by polynomials. Whatever their source, once polynomials enter the picture, notio...