Geometry of Uhlenbeck partial compactification of orthogonal instanton spaces and the K-theoretic Nekrasov partition functions
| Autor: | Choy, Jaeyoo |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $M^K_n$ be the moduli space of framed $K$-instantons over $S^4$ with instanton number $n$ when $K$ is a compact simple Lie group of classical type. Let $U^{K}_{n}$ be the Uhlenbeck partial compactification of $M^{K}_{n}$. A scheme structure on $U^{K}_{n}$ is endowed by Donaldson as an algebro-geometric Hamiltonian reduction of ADHM data. In this paper, for $K=SO(N,R)$, $N\ge5$, we prove that $U^{K}_{n}$ is an irreducible normal variety with smooth locus $M^{K}_{n}$. Hence, together with the author's previous result, the K-theoretic Nekrasov partition function for any simple classical group other than $SO(3,R)$, is interpreted as a generating function of Hilbert series of the instanton moduli spaces. Using this approach we also study the case $K=SO(4,R)$ which is the unique semisimple but non-simple classical group. Comment: 40 pages, v.2: typos corrected, v.3: dedicatory and acknowledgement messages added, references updated, to appear in Adv. Math |
| Databáze: | arXiv |
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