On Degeneration of the Surface in the Fitting Compactification of Moduli of Stable Vector Bundles
Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 143-150.

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A new compactification of the moduli scheme of Gieseker-stable vector bundles with given Hilbert polynomial on a smooth projective polarized surface $(S,\mathsf{H})$ over a field $k=\overline k$ of zero characteristic was constructed in previous papers by the author. Families of locally free sheaves on the surface $S$ are completed by the locally free sheaves on the schemes which are certain modifications of $S$. We describe the class of modified surfaces that appear in the construction.
Mots-clés : moduli space
Keywords: semistable coherent sheaf, locally free sheaf, blowup algebra, projective algebraic surface, ample divisor.
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N. V. Timofeeva. On Degeneration of the Surface in the Fitting Compactification of Moduli of Stable Vector Bundles. Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 143-150. http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a12/

[1] D. Gieseker, “On the moduli of vector bundles on an algebraic surface”, Ann. of Math. (2), 106:1 (1977), 45–60 | DOI | MR | Zbl

[2] G. Ellingsrud, L. Göttsche, “Variation of moduli spaces and Donaldson invariants under change of polarization”, J. Reine Angew. Math., 467 (1995), 1–49 | MR | Zbl

[3] M. Maruyama, “Moduli of stable sheaves. II”, J. Math. Kyoto Univ., 18:3 (1978), 557–614 | MR | Zbl

[4] N. V. Timofeeva, “Kompaktifikatsiya v skheme Gilberta mnogoobraziya modulei stabilnykh 2-vektornykh rassloenii na poverkhnosti”, Matem. zametki, 82:5 (2007), 756–769 | MR | Zbl

[5] N. V. Timofeeva, “O novoi kompaktifikatsii modulei vektornykh rassloenii na poverkhnosti”, Matem. sb., 199:7 (2008), 103–122 | MR

[6] N. V. Timofeeva, “O novoi kompaktifikatsii modulei vektornykh rassloenii na poverkhnosti. II”, Matem. sb., 200:3 (2009), 95–118 | MR | Zbl

[7] D. Eisenbud, Commutative Algebra. With a View Toward Algebraic Geometry, Grad. Texts in Math., 150, Springer-Verlag, New York, 1995 | MR | Zbl

[8] C. Okonek, M. Schneider, H. Spindler, Vector Bundles on Complex Projective Spaces, Progr. Math., 3, Birkhäuser, Boston, 1980 | MR | Zbl

[9] H. Hironaka, “Resolution of singularities of an algebraic variety over a field of characteristic zero: I”, Ann. of Math. (2), 79:1 (1964), 109–203 | DOI | MR | Zbl

[10] R. Khartskhorn, Algebraicheskaya geometriya, Mir, M., 1981 | MR | Zbl