Volume 20, issue 1 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 8, 3307–3833
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Stable pair invariants on Calabi–Yau threefolds containing $\mathbb{P}^2$

Yukinobu Toda

Geometry & Topology 20 (2016) 555–611
Bibliography
1 A Bayer, E Macrì, The space of stability conditions on the local projective plane, Duke Math. J. 160 (2011) 263 MR2852118
2 A Bayer, E Macrì, Y Toda, Bridgeland stability conditions on threefolds, I : Bogomolov–Gieseker type inequalities, J. Algebraic Geom. 23 (2014) 117 MR3121850
3 A Beauville, Some remarks on Kähler manifolds with c1 = 0, from: "Classification of algebraic and analytic manifolds" (editor K Ueno), Progr. Math. 39, Birkhäuser (1983) 1 MR728605
4 K Behrend, Gromov–Witten invariants in algebraic geometry, Invent. Math. 127 (1997) 601 MR1431140
5 K Behrend, Donaldson–Thomas type invariants via microlocal geometry, Ann. of Math. 170 (2009) 1307 MR2600874
6 O Ben-Bassat, C Brav, V Bussi, D Joyce, A ‘Darboux theorem’ for shifted symplectic structures on derived Artin stacks, with applications, Geom. Topol. 19 (2015) 1287 MR3352237
7 T Bridgeland, Flops and derived categories, Invent. Math. 147 (2002) 613 MR1893007
8 T Bridgeland, t-structures on some local Calabi–Yau varieties, J. Algebra 289 (2005) 453 MR2142382
9 T Bridgeland, Stability conditions on triangulated categories, Ann. of Math. 166 (2007) 317 MR2373143
10 T Bridgeland, Hall algebras and curve-counting invariants, J. Amer. Math. Soc. 24 (2011) 969 MR2813335
11 T Bridgeland, A King, M Reid, The McKay correspondence as an equivalence of derived categories, J. Amer. Math. Soc. 14 (2001) 535 MR1824990
12 K Bringmann, J Manschot, From sheaves on 2 to a generalization of the Rademacher expansion, Amer. J. Math. 135 (2013) 1039 MR3086068
13 J Bryan, C Cadman, B Young, The orbifold topological vertex, Adv. Math. 229 (2012) 531 MR2854183
14 J Bryan, T Graber, The crepant resolution conjecture, from: "Algebraic geometry—Seattle 2005, Part 1" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 23 MR2483931
15 J Bryan, D Steinberg, Curve counting invariants for crepant resolutions, Trans. Amer. Math. Soc. 368 (2016) 1583 MR3449219
16 V Bussi, Generalized Donaldson–Thomas theory over fields 𝕂, preprint (2014) arXiv:1403.2403
17 J Calabrese, Donaldson–Thomas invariants and flops, preprint (2014) arXiv:1111.1670
18 J Calabrese, On the crepant resolution conjecture for Donaldson–Thomas invariants, J. Algebraic Geom. 25 (2016) 1 MR3419955
19 T Coates, H Iritani, H H Tseng, Wall-crossings in toric Gromov–Witten theory, I : Crepant examples, Geom. Topol. 13 (2009) 2675 MR2529944
20 L Göttsche, The Betti numbers of the Hilbert scheme of points on a smooth projective surface, Math. Ann. 286 (1990) 193 MR1032930
21 L Göttsche, Theta functions and Hodge numbers of moduli spaces of sheaves on rational surfaces, Comm. Math. Phys. 206 (1999) 105 MR1736989
22 D Happel, I Reiten, S O Smalø, Tilting in abelian categories and quasitilted algebras, 575, Amer. Math. Soc. (1996) MR1327209
23 D Joyce, Configurations in abelian categories, II : Ringel–Hall algebras, Adv. Math. 210 (2007) 635 MR2303235
24 D Joyce, Configurations in abelian categories, IV : Invariants and changing stability conditions, Adv. Math. 217 (2008) 125 MR2357325
25 D Joyce, Y Song, A theory of generalized Donaldson–Thomas invariants, 1020, Amer. Math. Soc. (2012) MR2951762
26 G Kapustka, M Kapustka, Primitive contractions of Calabi–Yau threefolds, I, Comm. Algebra 37 (2009) 482 MR2493796
27 Y Kawamata, Log crepant birational maps and derived categories, J. Math. Sci. Univ. Tokyo 12 (2005) 211 MR2150737
28 A A Klyachko, Moduli of vector bundles and numbers of classes, Funktsional. Anal. i Prilozhen. 25 (1991) 81 MR1113131
29 J Kollár, S Mori, Birational geometry of algebraic varieties, 134, Cambridge Univ. Press (1998) MR1658959
30 M Kontsevich, Homological algebra of mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, Volume 1" (editor S D Chatterji), Birkhäuser (1995) 120 MR1403918
31 M Kontsevich, Y Soibelman, Stability structures, motivic Donaldson–Thomas invariants and cluster transformations, preprint (2008) arXiv:0811.2435
32 M Kool, Euler characteristics of moduli spaces of torsion free sheaves on toric surfaces, Geom. Dedicata 176 (2015) 241 MR3347580
33 M Lieblich, Moduli of complexes on a proper morphism, J. Algebraic Geom. 15 (2006) 175 MR2177199
34 M Lieblich, The openness of tilted hearts, (2013) MR2998828
35 J Manschot, The Betti numbers of the moduli space of stable sheaves of rank 3 on 2, Lett. Math. Phys. 98 (2011) 65 MR2836429
36 J Manschot, Sheaves on 2 and generalized Appell functions, preprint (2015) arXiv:1407.7785
37 D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory, I, Compos. Math. 142 (2006) 1263 MR2264664
38 T Milanov, Y Ruan, Y Shen, Gromov–Witten theory and cycle-valued modular forms, preprint (2012) arXiv:1206.3879
39 S Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982) 133 MR662120
40 A Okounkov, R Pandharipande, Virasoro constraints for target curves, Invent. Math. 163 (2006) 47 MR2208418
41 R Pandharipande, A Pixton, Gromov–Witten/pairs correspondence for the quintic 3–fold, preprint (2016) arXiv:1206.5490v2
42 R Pandharipande, R P Thomas, Curve counting via stable pairs in the derived category, Invent. Math. 178 (2009) 407 MR2545686
43 R Pandharipande, R P Thomas, Stable pairs and BPS invariants, J. Amer. Math. Soc. 23 (2010) 267 MR2552254
44 T Pantev, B Toën, M Vaquié, G Vezzosi, Shifted symplectic structures, Publ. Math. Inst. Hautes Études Sci. 117 (2013) 271 MR3090262
45 D Ross, Donaldson–Thomas theory and resolutions of toric transverse A–Singularities, preprint (2016) arXiv:1409.7011
46 R Rouquier, Dimensions of triangulated categories, J. K-Theory 1 (2008) 193 MR2434186
47 Y Ruan, The cohomology ring of crepant resolutions of orbifolds, from: "Gromov–Witten theory of spin curves and orbifolds" (editors T J Jarvis, T Kimura, A Vaintrob), Contemp. Math. 403, Amer. Math. Soc. (2006) 117 MR2234886
48 P Seidel, R Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001) 37 MR1831820
49 J Stoppa, R P Thomas, Hilbert schemes and stable pairs : GIT and derived category wall crossings, Bull. Soc. Math. France 139 (2011) 297 MR2869309
50 R P Thomas, A holomorphic Casson invariant for Calabi–Yau 3–folds, and bundles on K3 fibrations, J. Differential Geom. 54 (2000) 367 MR1818182
51 Y Toda, Moduli stacks and invariants of semistable objects on K3 surfaces, Adv. Math. 217 (2008) 2736 MR2397465
52 Y Toda, Limit stable objects on Calabi–Yau 3–folds, Duke Math. J. 149 (2009) 157 MR2541209
53 Y Toda, Curve counting theories via stable objects, I : DT/PT correspondence, J. Amer. Math. Soc. 23 (2010) 1119 MR2669709
54 Y Toda, Generating functions of stable pair invariants via wall-crossings in derived categories, from: "New developments in algebraic geometry, integrable systems and mirror symmetry" (editors M H Saito, S Hosono, K Yoshioka), Adv. Stud. Pure Math. 59, Math. Soc. Japan (2010) 389 MR2683216
55 Y Toda, Stable pairs on local K3 surfaces, J. Differential Geom. 92 (2012) 285 MR2998674
56 Y Toda, Curve counting theories via stable objects, II : DT/ncDT flop formula, J. Reine Angew. Math. 675 (2013) 1 MR3021446
57 Y Toda, Generalized Donaldson–Thomas invariants on the local projective plane, preprint (2014) arXiv:1405.3366
58 Y Toda, Gepner type stability conditions on graded matrix factorizations, Algebr. Geom. 1 (2014) 613 MR3296807
59 C Vafa, E Witten, A strong coupling test of S–duality, Nuclear Phys. B 431 (1994) 3 MR1305096
60 K Yoshioka, The Betti numbers of the moduli space of stable sheaves of rank 2 on P2, J. Reine Angew. Math. 453 (1994) 193 MR1285785
61 K Yoshioka, Chamber structure of polarizations and the moduli of stable sheaves on a ruled surface, Internat. J. Math. 7 (1996) 411 MR1395938