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- Title
Moduli spaces of stable quotients and wall-crossing phenomena.
- Authors
Toda, Yukinobu
- Abstract
The moduli space of holomorphic maps from Riemann surfaces to the Grassmannian is known to have two kinds of compactifications: Kontsevich’s stable map compactification and Marian–Oprea–Pandharipande’s stable quotient compactification. Over a non-singular curve, the latter moduli space is Grothendieck’s Quot scheme. In this paper, we give the notion of ‘ ϵ-stable quotients’ for a positive real number ϵ, and show that stable maps and stable quotients are related by wall-crossing phenomena. We will also discuss Gromov–Witten type invariants associated to ϵ-stable quotients, and investigate them under wall crossing.
- Subjects
MODULI theory; ALGEBRAIC spaces; QUOTIENT rings; HOLOMORPHIC functions; RIEMANN surfaces; GRASSMANN manifolds; COMPACTIFICATION (Mathematics); SCHEMES (Algebraic geometry)
- Publication
Compositio Mathematica, 2011, Vol 147, Issue 5, p1479
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X11005434