The connectedness of the moduli space of maps to homogeneous spaces
By B. Kim, R. Pandharipande. 2000
151 citations recorded by the source corpus.
We prove the connectedness of the moduli space of maps (of fixed genus and homology class) to the homogeneous space G/P by degeneration via the maximal torus action. In the genus 0 case, the irreducibility of the moduli of maps is a direct consequence of connectedness. An analysis of a related Bialynicki-Birula stratification of the map space yields a rationality result: the (coarse) moduli space of genus 0 maps to G/P is a rational variety. The rationality argument depends essentially upon rationality results for quotients of SL2 representations proven by Katsylo and Bogomolov.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/175574d05d03befa355b32c27381ceaae845f6fc
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In Geometry and Topology
- Anders Skovsted Buch
- P. Chaput
- Leonardo Constantin Mihalcea
- N. Perrin
- Harry Tamvakis
- Andrew Kresch
- Alexander Yong
- Hugh Thomas
In Mathematical Physics
- Anders Skovsted Buch
- Harry Tamvakis
- Andrew Kresch
- P. Chaput
- N. Perrin
- Leonardo Constantin Mihalcea
- Alexander Yong
- Damir Yeliussizov
Citations in the corpus
- Quantum cohomology of the Lagrangian Grassmannian (2003, background): “The open subscheme LMd ⊂ LQd, defined as the locus where E → OP1 ⊗ V has everywhere full rank, is smooth and irreducible, and coincides with the moduli space M0,3(LG, d) of 3-pointed (that is, parametrized) maps P(1) → LG of degree d (the irreducibility of all M0,i(LG, d) is known, [KP], [Th]).”
- Finiteness of cominuscule quantum K-theory (2010, background): “The space M0,n(X, d) is a projective variety with rational singularities, and it was proved by Kim and Pandharipande that this variety is also rational [17].”
- The moduli space of stable quotients (2009, unknown): “…mCj D . y j /C mCj : Here, mCj is the sum mCj D X J 0;J 00 J 0;J 00 ; for partitions J 0[J 00 D f1; : : : ;mC dg; mC j 2 J 0 fmC 1; : : : ;mC dg: The boundary divisor J 0;J 00 of SMg;mCd parameterizes curves C D C 0[C 00; g.C 0/D 0; g.C 00/D g with a single separating node and the markings…”
- QUANTUM K-THEORY OF GRASSMANNIANS (2008, background): “We finally give a “converse” to Lee and Pandharipande’s announcement from [40, p. 1379].”