no. 3
Flips of moduli of stable torsion free sheaves with c1=1 on ℙ2
[Flips de modules de faisceaux stables et sans torsion avec c1=1 sur ℙ2]
Bulletin de la Société Mathématique de France, Tome 142 (2014) no. 3, pp. 349-378

We study flips of moduli schemes of stable torsion free sheaves E with c1(E)=1 on ℙ2 via wall-crossing phenomena of Bridgeland stability conditions. They are described as stratified Grassmann bundles by a variation of stability of modules over certain finite dimensional algebra.

Nous étudions des flips de schémas de modules de faisceaux stables et sans torsion E avec c1(E)=1 sur ℙ2 à travers des phénomènes de traversée de mur des conditions de stabilité de Bridgeland. Ils sont décrits en tant que fibrés grassmanniens par une variation de stabilité de modules au-dessus d'une certaine algèbre de dimension finie.

DOI : 10.24033/bsmf.2668
Classification : 18E30, 14D20
Keywords: Bridgeland stability, moduli of vector bundles.
Mots-clés : Stabilité de Bridgeland, modules de fibrés vectoriels. 
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     author = {Ohkawa, Ryo},
     title = {Flips of moduli of stable torsion free sheaves with $c_1=1$ on~$\mathbb {P}^2$},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {349--378},
     year = {2014},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {142},
     number = {3},
     doi = {10.24033/bsmf.2668},
     mrnumber = {3295717},
     zbl = {1329.18014},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/bsmf.2668/}
}
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Ohkawa, Ryo. Flips of moduli of stable torsion free sheaves with $c_1=1$ on $\mathbb {P}^2$. Bulletin de la Société Mathématique de France, Tome 142 (2014) no. 3, pp. 349-378. doi: 10.24033/bsmf.2668

Arbarello, E.; Cornalba, M.; Griffiths, P.; Harris, J. Geometry of Algebraic curves, I, Springer, 1984 | MR | Zbl

Arcara, D.; Bertram, A.; Lieblich, M. Bridgeland-Stable Moduli Spaces for K -Trivial Surfaces, J. Eur. Math. Soc. (JEMS), Volume 15 (2013), pp. 1-38 | MR | Zbl

Birkar, C.; Cascini, P.; Hacon, C.; McKernan, J. Existence of minimal models for varieties of log general type, J. Amer. Math. Soc., Volume 23 (2010), pp. 405-468 | MR | Zbl | DOI

Bondal, A. I. Representation of associative algebras and coherent sheaves, Izv. Akad. Nauk SSSR Ser. Mat., Volume 53 (1989), pp. 25-44 English transl. in Math. USSR-Izv. 34(1):23-44, 1990. | MR | Zbl

Bridgeland, T. Stability conditions on triangulated categories, Ann. of Math., Volume 166 (2007), pp. 317-345 | MR | Zbl | DOI

Danilov, V. I.; Khovanskii, A. G. Newton polyhedra and an algorithm for calculating Hodge-Deligne numbers, Izv. Akad. Nauk SSSR Ser. Mat., Volume 50 (1986), pp. 925-945 English transl. in Math. USSR-Izv. 29(2):279-298, 1987. | MR | Zbl

Drézet, J. -M. Group de Picard des variétés de modules de faisceaux semi-stables sur ℙ2(ℂ), Ann. de l'Institut Fourier., Volume 38 (1988), pp. 105-168 | MR | Zbl | Numdam | DOI

Ellingsrud, G.; Strømme, S. A. Towards the Chow ring of the Hilbert scheme on ℙ2, J. reine angew. Math., Volume 441 (1993), pp. 33-44 | MR | Zbl

Huybrechts, D.; Lehn, M. Geometry of moduli spaces of sheaves, Aspects in Mathematics, E31, Vieweg, 1997 | MR | Zbl | DOI

Le Potier, J. À propos de la construction de l'espace de modules des faisceaux semi-stables sur le plan projectif, Bull. Soc. Math. France, Volume 122 (1994), pp. 363-369 | MR | Zbl | Numdam | DOI

Le Potier, J. Lectures on vector bundles, Cambridge Stud. Adv. Math, 54, Cambridge Univ. Press, 1997 | MR | Zbl

Li, J. Compactification of moduli of vector bundles over algebraic surfaces, World. Sci. Publishing, 1997, pp. 98-113 | MR | Zbl

Maruyama, M. On a compactification of a moduli space of stable vector bundles on a rational surface, Algebraic geometry and commutative algebra I, Kinokuniya, 1988, pp. 233-260 | MR | Zbl

Nakajima, H.; Yoshioka, K. Perverse coherent sheaves on blow-up. II. Wall-crossing and Betti numbers formula, J. Algebraic Geom., Volume 20 (2011), pp. 47-100 | MR | Zbl | DOI

Ohkawa, R. Moduli of Bridgeland semistable objects on ℙ2, Kodai Math. J, Volume 33 (2010), pp. 329-366 | MR | Zbl | DOI

Yoshioka, K. The Betti numbers of the moduli space of stable sheaves of rank 2 on ℙ2, J. reine angew, Math., Volume 453 (1994), pp. 193-220 | MR | Zbl

Yoshioka, K. A note on moduli of vector bundles on rational surfaces, J. Math. Kyoto Univ., Volume 43 (2003), pp. 139-163 | MR | Zbl

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