# Dennis Snow

Professor

B.A., Merrimack College, 1975

Ph.D., University of Notre Dame, 1979

Email: Dennis.M.Snow.1@nd.edu

Office: 142 Hayes-Healy Hall

Phone: (574) 631-7597

Fax: (574) 631-6579

For additional information see Dennis Snow’s Personal Page.

**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

Please direct questions and comments to: Dennis.M.Snow.1@nd.edu