Geometriae Dedicata

, Volume 177, Issue 1, pp 385–400 | Cite as

Affine pavings for moduli spaces of pure sheaves on \(\mathbb {P}^2\) with degree \(\le 5\)

  • Yao Yuan
Original Paper


Let \(M(d,r)\) be the moduli space of semistable sheaves of rank 0, Euler characteristic \(r\) and first Chern class \(dH~(d>0)\), with \(H\) the hyperplane class in \(\mathbb {P}^2\). In [14] we gave an explicit description of the class \([M(d,r)]\) of \(M(d,r)\) in the Grothendieck ring of varieties for \(d\le 5\) and \(g.c.d(d,r)=1\). In this paper we compute the fixed locus of \(M(d,r)\) under some \((\mathbb {C}^{*})^2\)-action and show that \(M(d,r)\) admits an affine paving for \(d\le 5\) and \(g.c.d(d,r)=1\). We also pose a conjecture that for any \(d\) and \(r\) coprime to \(d\), \(M(d,r)\) would admit an affine paving.


Moduli spaces of 1-dimensional semistable sheaves on the projective plan Affine pavings Cellular decompositions 

Mathematics Subject Classification




I was partially supported by NSFC grant 11301292. When I wrote this paper, I was a post-doc at MSC in Tsinghua University in Beijing. Finally I thank Y. Hu for some helpful discussions.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.MSCTsinghua UniversityBeijingChina

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