David Arends Gieseker (born 23 November 1943 in Oakland, California) is an American mathematician, specializing in algebraic geometry.
Gieseker received from Reed College in 1965 his bachelor's degree and from Harvard University in 1967 his master's degree and in 1970 his Ph.D. under Robin Hartshorne with thesis Contributions to the Theory of Positive Embeddings in Algebraic Geometry. Gieseker became in 1975 a professor at the University of California, Los Angeles.
- with Spencer Bloch: "The positivity of the Chern classes of an ample vector bundle". Inventiones mathematicae. 12 (2): 112–117. 1971. doi:10.1007/BF01404655.
- "On the moduli of vector bundles on an algebraic surface". Ann. of Math. 106 (2): 45–60. 1977. doi:10.2307/1971157.
- "Global moduli for surfaces of general type". Inventiones mathematicae. 43 (3): 233–282. 1977. doi:10.1007/BF01390081.
- "On a theorem of Bogomolov on Chern classes of stable bundles". American Journal of Mathematics. 101 (1): 77–85. 1979. doi:10.2307/2373939.
- "Stable curves and special divisors: Petri's conjecture". Inventiones mathematicae. 66 (2): 251–275. 1982. doi:10.1007/BF01389394.
- with Jun Li: "Irreducibility of moduli of rank two vector bundles". J. Differential Geom. 40: 23–104. 1994. doi:10.4310/jdg/1214455287.
- with Jun Li: "Moduli of high rank vector bundles over surfaces". J. Amer. Math. Soc. 9: 107–151. 1996. doi:10.1090/S0894-0347-96-00171-3.
- New Developments in Stability and Moduli, Conference in Honor of the 68th Birthday of David Gieseker, July 18–23, 2011, Hang-Zhou and Li Jiang, China