@article{TMF_2021_206_2_a6,
author = {A. I. Shchechkin},
title = {Blowup relations on $\mathbb{C}^2/\mathbb{Z}_2$ from {Nakajima{\textendash}Yoshioka} blowup relations},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {225--244},
year = {2021},
volume = {206},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2021_206_2_a6/}
}
TY - JOUR
AU - A. I. Shchechkin
TI - Blowup relations on $\mathbb{C}^2/\mathbb{Z}_2$ from Nakajima–Yoshioka blowup relations
JO - Teoretičeskaâ i matematičeskaâ fizika
PY - 2021
SP - 225
EP - 244
VL - 206
IS - 2
UR - http://geodesic.mathdoc.fr/item/TMF_2021_206_2_a6/
LA - ru
ID - TMF_2021_206_2_a6
ER -
A. I. Shchechkin. Blowup relations on $\mathbb{C}^2/\mathbb{Z}_2$ from Nakajima–Yoshioka blowup relations. Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 2, pp. 225-244. http://geodesic.mathdoc.fr/item/TMF_2021_206_2_a6/
[1] L. F. Alday, D. Gaiotto, Y. Tachikawa, “Liouville correlation functions from four-dimensional gauge theories”, Lett. Math. Phys., 91:2 (2010), 167–197, arXiv: 0906.3219 | DOI | MR | Zbl
[2] O. Gamayun, N. Iorgov, O. Lisovyy, “Conformal field theory of Painlevé VI”, JHEP, 10 (2012), 38, 24 pp., arXiv: ; Erratum, 183, 2 pp. 1207.0787 | DOI | MR | Zbl | DOI
[3] O. Gamayun, N. Iorgov, O. Lisovyy, “How instanton combinatorics solves Painlevé VI, V and IIIs”, J. Phys. A: Math. Theor., 46:33 (2013), 335203, 29 pp., arXiv: 1302.1832 | DOI | MR | Zbl
[4] M. Bershtein, A. Shchechkin, “$q$-deformed Painlevé $\tau$ function and $q$-deformed conformal blocks”, J. Phys. A: Math. Theor., 50:8 (2017), 085202, 22 pp., arXiv: 1608.02566 | DOI | MR | Zbl
[5] M. Jimbo, H. Nagoya, H. Sakai, “CFT approach to the $q$-Painlevé VI equation”, J. Integrable Syst., 2:1 (2017), xyx009, 27 pp., arXiv: 1706.01940 | MR | Zbl
[6] Y. Matsuhira, H. Nagoya, “Combinatorial expressions for the tau functions of $q$-Painlevé V and III equations”, SIGMA, 15 (2019), 074, 17 pp., arXiv: 1811.03285 | DOI
[7] P. Gavrylenko, “Isomonodromic $\tau$-functions and $W_N$ conformal blocks”, JHEP, 09 (2015), 167, 23 pp., arXiv: 1505.00259 | DOI | MR | Zbl
[8] N. Iorgov, O. Lisovyy, J. Teschner, “Isomonodromic $\tau$ functions from Liouville conformal blocks”, Commun. Math. Phys., 336:2 (2015), 671–694, arXiv: 1401.6104 | DOI | MR | Zbl
[9] M. Bershtein, A. Shchechkin, “Bilinear equations on Painlevé tau functions from CFT”, Commun. Math. Phys., 339:3 (2015), 1021–1061, arXiv: 1406.3008 | DOI | MR | Zbl
[10] M. Bershtein, A. Shchechkin, “Bäcklund transformation of Painlevé III($D_8$) $\tau$ function”, J. Phys. A: Math. Theor., 50:11 (2017), 115205, 31 pp., arXiv: 1608.02568 | DOI | MR | Zbl
[11] H. Nakajima, K. Yoshioka, “Instanton counting on blowup. II. K-theoretic partition function”, Transform. Groups, 10:3–4 (2005), 489–519, arXiv: math/0505553 | DOI | MR | Zbl
[12] G. Bonelli, K. Maruyoshi, A. Tanzini, “Instantons on ALE spaces and super Liouville conformal field theories”, JHEP, 08 (2011), 056, 9 pp., arXiv: 1106.2505 | DOI | MR | Zbl
[13] U. Bruzzo, M. Pedrini, F. Sala, R. Szabo, “Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces”, Adv. Math., 288 (2016), 1175–1308, arXiv: 1312.5554 | DOI | MR | Zbl
[14] M. Bershtein, A. Shchechkin, “Painlevé equations from Nakajima–Yoshioka blowup relations”, Lett. Math. Phys., 109:11 (2019), 2359–2402, arXiv: 1811.04050 | DOI | MR | Zbl
[15] M. Bershtein, P. Gavrylenko, A. Marshakov, “Cluster integrable systems, $q$-Painlevé equations and their quantization”, JHEP, 02 (2018), 077, 33 pp., arXiv: 1711.02063 | DOI | MR | Zbl
[16] M. A. Bershtein, P. G. Gavrilenko, A. V. Marshakov, “Klasternye tsepochki Tody i funktsii Nekrasova”, TMF, 198:2 (2019), 179–214 | DOI | DOI
[17] L. Göttshe, H. Nakajima, K. Yoshioka, “$K$-theoretic Donaldson invariants via instanton counting”, Pure Appl. Math. Quart., 5:3 (2009), 1029–1111, arXiv: math/0611945 | DOI | MR
[18] R. Fintushel, R. J. Stern, “The blowup formula for Donaldson invariants”, Ann. Math., 143:3 (1996), 529–546, arXiv: alg-geom/9405002 | DOI | MR | Zbl
[19] R. Brussee, Blow-up formulas for $(-2)$-spheres, arXiv: dg-ga/9412004
[20] H. Nakajima, K. Yoshioka, “Lectures on instanton counting”, Algebraic Structure (McGill University, Montréal, Canada, July 14–20, 2003), CRM Proceedings Lecture Notes, 38, eds. J. Hurtubise, E. Markman, AMS, Providence, RI, 2004, 31–101, arXiv: math/0311058 | DOI | MR | Zbl
[21] A. Its, O. Lisovyy, Yu. Tykhyy, “Connection problem for the sine-Gordon/Painlevé III tau function and irregular conformal blocks”, Int. Math. Res. Not., 2015:18 (2015), 8903–8924, arXiv: 1403.1235 | DOI | MR | Zbl
[22] G. Felder, M. Müller-Lennert, “Analyticity of Nekrasov partition functions”, Commun. Math. Phys., 364:2 (2018), 683–718, arXiv: 1709.05232 | DOI | MR | Zbl
[23] H. Nakajima, K. Yoshioka, “Perverse coherent sheaves on blow-up, III: Blow-up formula from wall-crossing”, Kyoto J. Math., 51:2 (2011), 263–335, arXiv: 0911.1773 | DOI | MR | Zbl
[24] A. Iqbal, A. K. Kashani-Poor, “Instanton counting and Chern–Simons theory”, Adv. Theor. Math. Phys., 7:3 (2003), 457–497, arXiv: hep-th/0212279 | DOI | MR | Zbl