Geodesic
Zero dimensional Donaldson–Thomas invariants of threefolds
Li, Jun1
1 Department of Mathematics, Stanford University, Stanford, CA 94305, USA
Geometry & topology, Tome 10 (2006) no. 4, pp. 2117-2171.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Using a homotopy approach, we prove in this paper a conjecture of Maulik, Nekrasov, Okounkov and Pandharipande on the dimension zero Donaldson–Thomas invariants of all smooth complex threefolds.

DOI : 10.2140/gt.2006.10.2117
Keywords: moduli space, Hilbert schemes, virtual cycle

Li, Jun 1

1 Department of Mathematics, Stanford University, Stanford, CA 94305, USA 
@article{GT_2006_10_4_a2,
     author = {Li, Jun},
     title = {Zero dimensional {Donaldson{\textendash}Thomas} invariants of threefolds},
     journal = {Geometry & topology},
     pages = {2117--2171},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2006},
     doi = {10.2140/gt.2006.10.2117},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2006.10.2117/}
}
TY  - JOUR
AU  - Li, Jun
TI  - Zero dimensional Donaldson–Thomas invariants of threefolds
JO  - Geometry & topology
PY  - 2006
SP  - 2117
EP  - 2171
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2006.10.2117/
DO  - 10.2140/gt.2006.10.2117
ID  - GT_2006_10_4_a2
ER  - 
%0 Journal Article
%A Li, Jun
%T Zero dimensional Donaldson–Thomas invariants of threefolds
%J Geometry & topology
%D 2006
%P 2117-2171
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2006.10.2117/
%R 10.2140/gt.2006.10.2117
%F GT_2006_10_4_a2
Li, Jun. Zero dimensional Donaldson–Thomas invariants of threefolds. Geometry & topology, Tome 10 (2006) no. 4, pp. 2117-2171. doi : 10.2140/gt.2006.10.2117. http://geodesic.mathdoc.fr/articles/10.2140/gt.2006.10.2117/

[1] I V Artamkin, On the deformation of sheaves, Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988) 660

[2] K Behrend, Donaldson-Thomas invariants via microlocal geometry

[3] K Behrend, B Fantechi, Symmetric obstruction theories and Hilbert schemes of points on threefolds

[4] K Behrend, B Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997) 45

[5] S K Donaldson, R P Thomas, Gauge theory in higher dimensions, from: "The geometric universe science, geometry, and the work of Roger Penrose (Oxford, 1996)" (editors S S Huggett, e al), Oxford Univ. Press (1998) 31

[6] M Levine, R Pandharipande, Algebraic Cobordism revisited

[7] J Li, G Tian, Virtual moduli cycles and Gromov–Witten invariants of algebraic varieties, J. Amer. Math. Soc. 11 (1998) 119

[8] J Li, G Tian, Comparison of algebraic and symplectic Gromov–Witten invariants, Asian J. Math. 3 (1999) 689

[9] M Maruyama, Moduli of stable sheaves II, J. Math. Kyoto Univ. 18 (1978) 557

[10] D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory I

[11] D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory II

[12] S Mukai, Symplectic structure of the moduli space of sheaves on an abelian or $K3$ surface, Invent. Math. 77 (1984) 101

[13] R P Thomas, A holomorphic Casson invariant for Calabi–Yau 3–folds, and bundles on $K3$ fibrations, J. Differential Geom. 54 (2000) 367

Cité par Sources :