Abstract:
A new compactification for the scheme of moduli for Gieseker-stable vector bundles with prescribed Hilbert polynomial on the smooth projective polarized surface (S,L) is constructed. We work over the field k=¯k of characteristic zero. Families of locally free sheaves on the surface S are completed with locally free sheaves on schemes which are modifications of S. The Gieseker-Maruyama moduli space has a birational
morphism onto the new moduli space. We propose the functor for families of pairs ‘polarized scheme-vector bundle’ with moduli space of such type.
Bibliography: 16 titles.
Citation:
N. V. Timofeeva, “On a new compactification of moduli of vector bundles on a surface.
III: Functorial approach”, Sb. Math., 202:3 (2011), 413–465
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\by N.~V.~Timofeeva
\paper On a new compactification of moduli of vector bundles on a surface.
III: Functorial approach
\jour Sb. Math.
\yr 2011
\vol 202
\issue 3
\pages 413--465
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This publication is cited in the following 11 articles:
N. V. Timofeeva, “Stability and equivalence of admissible pairs of arbitrary dimension for a compactification of the moduli space of stable vector bundles”, Theoret. and Math. Phys., 212:1 (2022), 984–1000
N. V. Timofeeva, “Locally Free Resolution of Coherent Sheaves in Arbitrary Dimension”, Math. Notes, 110:4 (2021), 632–637
N. V. Timofeeva, “Admissible pairs vs Gieseker-Maruyama”, Sb. Math., 210:5 (2019), 731–755
V. Baranovsky, “Uhlenbeck compactification as a functor”, Int. Math. Res. Not. IMRN, 2015:23 (2015), 12678–12712
N. V. Timofeeva, “On a morphism of compactifications of moduli scheme of vector bundles”, Sib. elektron. matem. izv., 12 (2015), 577–591
N. V. Timofeeva, “Izomorfizm kompaktifikatsii modulei vektornykh rassloenii: neprivedennye skhemy modulei”, Model. i analiz inform. sistem, 22:5 (2015), 629–647
N. V. Timofeeva, “On an Isomorphism of Compactifications of Moduli Scheme of Vector Bundles”, Model. anal. inf. sist., 19:1 (2015), 37
N. V. Timofeeva, “On a new compactification of moduli of vector bundles on a surface. IV: Nonreduced moduli”, Sb. Math., 204:1 (2013), 133–153
N. V. Timofeeva, “On a new compactification of moduli of vector bundles on a surface. V: Existence of a universal family”, Sb. Math., 204:3 (2013), 411–437
N. V. Timofeeva, “Ob odnom izomorfizme kompaktifikatsii skhemy modulei vektornykh rassloenii”, Model. i analiz inform. sistem, 19:1 (2012), 37–50
Markushevich D., Tikhomirov A.S., Trautmann G., “Bubble tree compactification of moduli spaces of vector bundles on surfaces”, Centr. Eur. J. Math., 10:4 (2012), 1331–1355
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