×
Mehta, V. B.; Ramanathan, A.

Semistable sheaves on projective varieties and their restriction to curves. (English) Zbl 0473.14001

Math. Ann. 258, 213-224 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0473.14001

Cited in 5 Reviews
Cited in 72 Documents

MSC:

14D20 Algebraic moduli problems, moduli of vector bundles
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14H10 Families, moduli of curves (algebraic)

Keywords:

torsion free coherent sheaf; semistable sheaf; restriction of sheaves to curves
Cite Review PDF
Full Text: DOI EuDML

References:

[1] Altman, A., Kleiman, S.: Introduction to Grothendieck duality theory. Lecture Notes in MathematicsVol. 146. Berlin, Heidelberg, New York: Springer 1970 · Zbl 0215.37201
[2] Bourbaki, N.: El?ments de math?matique. Alg?bre commutative, Chap. 7. Paris: Hermann 1965
[3] Grothendieck, A.: Technique de descente et th?or?mes d’existence en g?ometri? alg?brique. IV. Les sch?mas de Hilbert. S?minaire Bourbaki 1960/61, expos? 221
[4] Grothendieck, A., Dieudonn?, J.: El?ment de g?om?trie alg?briques, IV/3, IV/4. In: Publ. Math. I.H.E.S.28 (1966);32 (1967) (cited EGA)
[5] Harder, G., Narasimhan, M.S.: On the cohomology groups of moduli spaces of vector bundles on curves. Math. Ann.212, 215-248 (1975) · Zbl 0324.14006 · doi:10.1007/BF01357141
[6] Hartshorne, R.: Algebraic geometry. Graduate Texts in Mathematics, Vol. 52. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0367.14001
[7] Langton, S.: Valuative criteria for families of vector bundles on algebraic varieties. Ann. Math.101, 88-110 (1975) · Zbl 0307.14007 · doi:10.2307/1970987
[8] Maruyama, M.: Openness of a family of torsion free sheaves. J. Math. Kyoto Univ.16, 627-637 (1976) · Zbl 0404.14004
[9] Maruyama M.: The theorem of Grauert-Mullich-Spindler. Math. Ann.255, 317-333 (1981) · doi:10.1007/BF01450706
[10] Mumford, D.: Lectures on curves on an algebraic surface. Princeton: Princeton University Press 1966 · Zbl 0187.42701
[11] Mumford, D.: Abelian varieties. Bombay: Oxford University Press 1974 · Zbl 0326.14012
[12] Narasimhan, M.S., Ramanathan, A.: Openness of the semistability condition (preprint)
[13] Narasimhan, M.S., Seshadri C.S.: Stable and unitary bundles on compact Riemann surfaces. Ann. Math.82, 540-567 (1965) · Zbl 0171.04803 · doi:10.2307/1970710
[14] Okonek, C., Schneider, M., Spindler, H.: Vector bundles on complex projective spaces. Progress in Mathematics, Vol. 3. Basel: Birkh?user 1980 · Zbl 0438.32016
[15] Ramanan S., Ramanathan, A.: Some remarks on the instability flag (preprint) · Zbl 0567.14027
[16] Weil, A.: Sur les crit?res d’equivalence en g?om?trie alg?brique. Math. Ann.128, 95-127. Also in: Collected Works Vol. II, pp. 127-159. Berlin, Heidelberg, New York: Springer 1979 · Zbl 0057.13002 · doi:10.1007/BF01360127
[17] Zariski, O.: Introduction to the problem of minimal models in the theory of algebraic surfaces. The Mathematical Society of Japan 1958 · Zbl 0093.33904
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.