Equivariant map

About: Equivariant map is a research topic. Over the lifetime, 9205 publications have been published within this topic receiving 137115 citations.

K-theory Schubert calculus of the affine Grassmannian

Abstract: We construct the Schubert basis of the torus-equivariant K-homology of the affine Grassmannian of a simple algebraic group G, using the K-theoretic NilHecke ring of Kostant and Kumar. This is the K-theoretic analogue of a construction of Peterson in equivariant homology. For the case G = SL_n, the K-homology of the affine Grassmannian is identified with a sub-Hopf algebra of the ring of symmetric functions. The Schubert basis is represented by inhomogeneous symmetric functions, called K-k-Schur functions, whose highest degree term is a k-Schur function. The dual basis in K-cohomology is given by the affine stable Grothendieck polynomials, verifying a conjecture of Lam. In addition, we give a Pieri rule in K-homology. Many of our constructions have geometric interpretations using Kashiwara's thick affine flag manifold.

Submersions and equivariant Quillen metrics

Abstract: Dans cet article, on calcule le comportement de la metrique de Quillen equivariante par snbmersions. On etend ainsi une formule

Exact results for N = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants

Abstract: We provide a contour integral formula for the exact partition function of $$ \mathcal{N} $$ = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) $$ \mathcal{N} $$ = 2∗ theory on $$ {\mathrm{\mathbb{P}}}^2 $$ for all instanton numbers. In the zero mass case, corresponding to the $$ \mathcal{N} $$ = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

Birational cobordisms and factorization of birational maps

Abstract: In this paper we develop a Morse-like theory in order to decompose birational maps and morphisms of smooth projective varieties defined over a field of characteristic zero into more elementary steps which are locally \'etale isomorphic to equivariant flips, blow-ups and blow-downs of toric varieties A crucial role in the considerations is played by K^*-actions where K is the base field This paper serves as a basis for proving the weak factorization conjecture on factorization of birational maps in characteristic zero into blow-ups and blow-downs This is carried out in two subsequent papers, one by the author (Combinatorial structures on toroidal varieties: a proof of the weak Factorization Theorem) and one joint with Abramovich, Karu and Matsuki (Torification and factorization of birational maps) In the last paper, the ideas of the present paper are discussed using geometric invariant theory