Abstract:
A new compactification of the moduli scheme of Gieseker-stable vector bundles with given Hilbert polynomial on a smooth projective polarized surface (S,H) over a field k=¯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.
Citation:
N. V. Timofeeva, “On Degeneration of the Surface in the Fitting Compactification of Moduli of Stable Vector Bundles”, Mat. Zametki, 90:1 (2011), 143–150; Math. Notes, 90:1 (2011), 142–148
\Bibitem{Tim11}
\by N.~V.~Timofeeva
\paper On Degeneration of the Surface in the Fitting Compactification of Moduli of Stable Vector Bundles
\jour Mat. Zametki
\yr 2011
\vol 90
\issue 1
\pages 143--150
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\crossref{https://doi.org/10.4213/mzm6321}
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\transl
\jour Math. Notes
\yr 2011
\vol 90
\issue 1
\pages 142--148
\crossref{https://doi.org/10.1134/S0001434611070145}
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Linking options:
https://www.mathnet.ru/eng/mzm6321
https://doi.org/10.4213/mzm6321
https://www.mathnet.ru/eng/mzm/v90/i1/p143
This publication is cited in the following 10 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
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
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