The Singular Supports of IC sheaves on Quasimaps' Spaces are Irreducible

1997/05/01 by Michael Finkelberg, Alexander Kuznetsov, Finkelberg, Michael +3
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9705003

8 pages, AmsLatex 1.1

arxiv created 1997/05/01 · arxiv updated 2009/11/30

Abstract

Let C be a smooth projective curve of genus 0. Let B be the variety of complete flags in an n-dimensional vector space V. Given an (n-1)-tuple α∈ N[I] of positive integers one can consider the space Q_α of algebraic maps of degree α from C to B. This space admits some remarkable compactifications Q^D_α (Quasimaps), Q^L_α (Quasiflags) constructed by Drinfeld and Laumon respectively. In [Kuznetsov] it was proved that the natural map π: Q^L_α→ Q^D_α is a small resolution of singularities. The aim of the present note is to study the singular support of the Goresky-MacPherson sheaf IC_α on the Quasimaps' space Q^D_α. Namely, we prove that this singular support SS(IC_α) is irreducible. The proof is based on the factorization property of Quasimaps' space and on the detailed analysis of Laumon's resolution π: Q^L_α→ Q^D_α.

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