Dennis Snow

Professor

Education

B.A., Merrimack College, 1975
Ph.D., University of Notre Dame, 1979

Research Groups

Algebra and Algebraic Geometry, Analysis and Partial Differential Equations

Research Area

Complex Analysis, Complex Geometry

Bio

Research Interests

My research is centered on the study of complex manifolds and Lie groups of holomorphic automorphisms acting on them. This work has primarily involved homogeneous complex manifolds—-their classification, computing numerical invariants, and establishing various vanishing theorems for their cohomology. I have also been interested in analyzing the quotients of complex manifolds by the actions of Lie groups.

My most recent work determines bounds for the anticanonical bundle and the dimension of the holomorphic automorphism group of a homogeneous compact complex manifold.

Selected Publications

• D. Snow, Reductive group actions on Stein spaces, Math. Ann. 259 (1982), 79-97.
• D. Snow, Invariant complex structures on reductive Lie groups, J. Reine Angew. Math. 371 (1986), 191-215.
• D. Snow, Cohomology of twisted holomorphic forms on Grassmann manifolds and quadric hypersurfaces, Math. Ann. 276 (1986), 159-176.
• D. Snow, Vanishing theorems on compact Hermitian symmetric spaces, Math. Z. 198 (1988), 1-20.
• D. Snow, Weyl group orbits, ACM Trans. Math. Software 16 (1990), 94-108.
• Dennis M. Snow. The nef value of homogeneous line bundles and related vanishing theorems. _Forum Math., _ 7 (1995) 385-392.
• L. Manivel and D. Snow, A Borel-Weil theorem for holomorphic forms, Compositio Math. 103 (1996), 351-365.
• D. Snow and J. Winkelmann, Compact complex homogeneous manifolds with large automorphism groups, Invent. Math. 134 (1998), 139-144.
• D. Snow, The role of exotic affine spaces in the classification of homogeneous affine varieties, In: Algebraic Transformation Groups and Algebraic Varieties, Encyclopaedia of Mathematical Sciences, Vol. 132, Springer Verlag, 2004. pdf
• D. Snow, A bound for the dimension of the automorphism group of a homogeneous compact complex manifold, Proc. Amer. Math. Soc. 132 (2004), 2051—2055. pdf
• D. Snow, Bounds for the anticanonical bundle of a homogeneous projective rational manifold, Documenta Math. 9 (2004), 251—263. pdf