Instanton bundles on two Fano threefolds of index 1
-
Gianfranco Casnati
and
Ozhan Genc
Abstract
We deal with instanton bundles on the product
Funding source: Ministero dell’Istruzione, dell’Università e della Ricerca
Award Identifier / Grant number: E11G18000350001
Funding source: Narodowe Centrum Nauki
Award Identifier / Grant number: 2018/30/E/ST1/00530
Funding statement: The first author is a member of GNSAGA group of INdAM, of PRIN 2015 “Geometry of Algebraic Varieties”, cofinanced by MIUR and is supported by the framework of the MIUR grant Dipartimenti di Eccellenza 2018–2022 (E11G18000350001). The second author is supported by Narodowe Centrum Nauki 2018/30/E/ST1/00530.
Acknowledgements
The authors would like to express their thanks to the referee for her/his criticisms, questions, remarks and suggestions which have considerably improved the whole exposition.
References
[1] V. Ancona and G. Ottaviani, Canonical resolutions of sheaves on Schubert and Brieskorn varieties, Complex Analysis (Wuppertal 1991), Aspects Math. E17, Friedrich Vieweg, Braunschweig (1991), 14–19. 10.1007/978-3-322-86856-5_3Search in Google Scholar
[2] V. Antonelli and F. Malaspina, Instanton bundles on the Segre threefold with Picard number three, preprint (2019), https://arxiv.org/abs/1909.10895; to appear in Math. Nachr. 10.1002/mana.201900190Search in Google Scholar
[3] E. Arrondo, A home-made Hartshorne–Serre correspondence, Rev. Mat. Complut. 20 (2007), no. 2, 423–443. 10.5209/rev_REMA.2007.v20.n2.16502Search in Google Scholar
[4] M. F. Atiyah, N. J. Hitchin, V. G. Drinfel’d and Y. I. Manin, Construction of instantons, Phys. Lett. A 65 (1978), no. 3, 185–187. 10.1142/9789812794345_0018Search in Google Scholar
[5]
G. Casnati, E. Coskun, O. Genc and F. Malaspina,
Instanton bundles on the blow up of
[6] D. Faenzi, Even and odd instanton bundles on Fano threefolds of Picard number one, Manuscripta Math. 144 (2014), no. 1–2, 199–239. 10.1007/s00229-013-0646-6Search in Google Scholar
[7] R. Hartshorne, Algebraic Geometry, Grad. Texts in Math. 52, Springer, New York, 1977. 10.1007/978-1-4757-3849-0Search in Google Scholar
[8] R. Hartshorne, Coherent functors, Adv. Math. 140 (1998), no. 1, 44–94. 10.1006/aima.1998.1762Search in Google Scholar
[9]
H. J. Hoppe,
Generischer Spaltungstyp und zweite Chernklasse stabiler Vektorraumbündel vom Rang 4 auf
[10] V. A. Iskovskikh and Y. G. Prokhorov, Fano varieties, Algebraic Geometry. V, Encyclopaedia Math. Sci. 47, Springer, Berlin (1999), 1–247. Search in Google Scholar
[11] M. Jardim, G. Menet, D. M. Prata and H. N. Sá Earp, Holomorphic bundles for higher dimensional gauge theory, Bull. Lond. Math. Soc. 49 (2017), no. 1, 117–132. 10.1112/blms.12017Search in Google Scholar
[12] A. Kuznetsov, Instanton bundles on Fano threefolds, Cent. Eur. J. Math. 10 (2012), no. 4, 1198–1231. 10.2478/s11533-012-0055-1Search in Google Scholar
[13] R. Lazarsfeld, Positivity in Algebraic Geometry. II. Positivity for Vector Bundles, and Multiplier Ideals, Ergeb. Math. Grenzgeb. (3) 49, Springer, Berlin, 2004. 10.1007/978-3-642-18810-7Search in Google Scholar
[14]
F. Malaspina, S. Marchesi and J. Pons–Llopis,
Instanton bundles on the flag variety
[15] M. Maruyama, Boundedness of semistable sheaves of small ranks, Nagoya Math. J. 78 (1980), 65–94. 10.1017/S002776300001881XSearch in Google Scholar
[16] D. O. Orlov, Projective bundles, monoidal transformations, and derived categories of coherent sheaves (in Russian), Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992), no. 4, 852–862; translation in Russian Acad. Sci. Izv. Math. 41 (1993), 133–141. 10.1070/IM1993v041n01ABEH002182Search in Google Scholar
[17]
A. S. Tikhomirov,
Moduli of mathematical instanton vector bundles with odd
[18]
A. S. Tikhomirov,
Moduli of mathematical instanton vector bundles with even
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Articles in the same Issue
- Frontmatter
- Conjugacy classes and automorphisms of twin groups
- Decomposition and classification of length functions
- Successive coefficients of close-to-convex functions
- Frobenius cowreaths and Morita contexts
- The non-linear sewing lemma III: Stability and generic properties
- On hyperquadrics containing projective varieties
- Explicit Burgess-like subconvex bounds for GL2 × GL1
- Characterisation of polyhedral products with finite generalised Postnikov decomposition
- Solvable Lie and Leibniz superalgebras with a given nilradical
- Alvis–Curtis duality for representations of reductive groups with Frobenius maps
- The third partial cohomology group and existence of extensions of semilattices of groups by groups
- Instanton bundles on two Fano threefolds of index 1
- Carleson measure characterizations of the Campanato type space associated with Schrödinger operators on stratified Lie groups
Articles in the same Issue
- Frontmatter
- Conjugacy classes and automorphisms of twin groups
- Decomposition and classification of length functions
- Successive coefficients of close-to-convex functions
- Frobenius cowreaths and Morita contexts
- The non-linear sewing lemma III: Stability and generic properties
- On hyperquadrics containing projective varieties
- Explicit Burgess-like subconvex bounds for GL2 × GL1
- Characterisation of polyhedral products with finite generalised Postnikov decomposition
- Solvable Lie and Leibniz superalgebras with a given nilradical
- Alvis–Curtis duality for representations of reductive groups with Frobenius maps
- The third partial cohomology group and existence of extensions of semilattices of groups by groups
- Instanton bundles on two Fano threefolds of index 1
- Carleson measure characterizations of the Campanato type space associated with Schrödinger operators on stratified Lie groups
