Inaba, Michi-Aki On the moduli of stable sheaves on a reducible projective scheme and examples on a reducible quadric surface. (English) Zbl 1056.14014 Nagoya Math. J. 166, 135-181 (2002). Summary: We study the moduli space of stable sheaves on a reducible projective scheme by use of a suitable stratification of the moduli space. Each stratum is the moduli space of “triples”, which is the main object investigated in this paper. As an application, we can see that the relative moduli space of rank two stable sheaves on quadric surfaces gives a nontrivial example of the relative moduli space which is not flat over the base space. Cited in 5 Documents MSC: 14D20 Algebraic moduli problems, moduli of vector bundles 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli Keywords:stratification; relative moduli space PDF BibTeX XML Cite \textit{M.-A. Inaba}, Nagoya Math. J. 166, 135--181 (2002; Zbl 1056.14014) Full Text: DOI References: [1] J. Math. Kyoto Univ. 33 pp 451– (1993) · Zbl 0798.14006 · doi:10.1215/kjm/1250519269 [2] Compos. Math. 98 pp 305– (1995) [3] DOI: 10.1007/BF02698887 · Zbl 0891.14005 · doi:10.1007/BF02698887 [4] Fibres vectoriels sur les courbes algébriques, Astérisque, 96, Société Mathématique de France (1982) [5] DOI: 10.1016/0001-8708(77)90041-X · Zbl 0371.14009 · doi:10.1016/0001-8708(77)90041-X [6] Lecture Notes in Pure and Appl. Math. 179 (1996) [7] J. Reine Angew. Math. 453 pp 113– (1994) [8] J. Math. Kyoto Univ. 18 pp 557– (1978) · Zbl 0395.14006 · doi:10.1215/kjm/1250522511 [9] Vector bundles on complex projective spaces (1980) · Zbl 0438.32016 [11] DOI: 10.1090/S0002-9947-1979-0536936-4 · doi:10.1090/S0002-9947-1979-0536936-4 [13] Proc. Indian Acad. Sci. 107 pp 101– (1997) [14] J. Math. Kyoto Univ. 40 pp 119– (2000) · Zbl 1002.14002 · doi:10.1215/kjm/1250517762 [15] Geometric invariant theory (1965) [16] Chaps. I,II,III,IV, Inst. Hautes Etudes Sci. Publ. Math. No. 4,8,11,17,20,24,28,32 pp 1960– [17] J. Differential Geom. 40 pp 23– (1994) · Zbl 0827.14008 · doi:10.4310/jdg/1214455287 [18] DOI: 10.1007/BF01446303 · Zbl 0847.14018 · doi:10.1007/BF01446303 [19] DOI: 10.1016/0001-8708(80)90043-2 · Zbl 0427.14015 · doi:10.1016/0001-8708(80)90043-2 [20] DOI: 10.1093/qmath/36.2.159 · Zbl 0575.14013 · doi:10.1093/qmath/36.2.159 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.