Geometric Proofs of Some Results of Morita

An algebro-geometric proof of Witten's conjecture

We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumerating ramified coverings of the 2-sphere.

A short geometric proof of a conjecture of Fulton

We give a new geometric proof of a conjecture of Fulton on the Littlewood-Richardson coefficients. This conjecture was firstly proved by Knutson, Tao and Woodward using the Honeycomb theory. A geometric proof was given by Belkale. Our proof is based on the geometry of Horn's cones.

Christoph定理的代数几何证明

Algebro-geometric proof of Christoph's Theorem

本文通过代数方法证明了Christoph定理，该定理表明存在有限自动机可计算代数函数级数的系数。

A geometric proof of the classification of complex vector cross product

In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.

Geometric Proof of a Conjecture of Fulton

We give a geometric proof of a conjecture of W. Fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for GL(r).

射影超曲面的多点虚拟结构常数的广义镜像变换的几何证明

Geometrical Proof of Generalized Mirror Transformation for Multi-Point Virtual Strucutre Constants of Projective Hypersurfaces

本文通过几何方法证明了CP^{N-1}中k次超曲面的多点虚拟结构常数的广义镜像变换。

A geometric proof of an equivariant Pieri rule for flag manifolds

We use geometry to give a short proof of an equivariant Pieri rule in the classical flag manifold. This rule is due to Robinson, who gave an algebraic proof.

Geometric Proofs of Horn and Saturation Conjectures

We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of Horn and saturation conjectures. We also establish transversality theorems for Schubert calculus in non-zero characteristic. Some parts of the version posted in Nov 2002 (concerning explicit invariants constructed from Schubert calculus) have been removed from this version. They have appeared separately in IMRN 2004, no. 69, pages 3709--3721 " Invariant theory of GL(n) and Intersection theory of Grassma…

A geometric proof of Duflo's Theorem

Let $R$ be a commutative ring: we explain the Beilinson-Bernstein localisation mechanism for sheaves of homogeneous twisted differential operators defined over a smooth, separated, locally of finite type $R$-scheme. As an application, we give a new proof of Duflo's theorem characterising the primitive ideals of the enveloping algebra of a complex semisimple Lie algebra.

Geometric proofs of theorems of Ax-Kochen and Ersov

We give an algebraic geometric proof of the Theorem of Ax and Kochen on p-adic diophantine equations in many variables. Unlike Ax-Kochen's proof, ours does not use any notions from mathematical logic and is based on weak toroidalization of morphisms. We also show how this geometric approach yields new proofs of the Ax-Kochen-Ersov transfer principle for local fields, and of quantifier elimination theorems of Basarab and Pas.

A short proof that all linear codes are weakly algebraic-geometric using Bertini theorems of B. Poonen

In this paper we give a simpler proof of a deep theorem proved by Pellikan, Shen and van Wee that all linear codes are weakly algebraic-geometric using a theorem of B.Poonen.

A Geometric Proof of the Feigin-Frenkel Theorem

We reprove the theorem of Feigin and Frenkel relating the center of the critical level enveloping algebra of the Kac-Moody algebra for a semisimple Lie algebra to opers (which are certain de Rham local systems with extra structure) for the Langlands dual group. Our proof incorporates a construction of Beilinson and Drinfeld relating the Feigin-Frenkel isomorphism to (more classical) Langlands duality through the geometric Satake theorem.