Herbert Clemens

Herbert Clemens
Born	15 August 1939 (1939-08-15) (age 84) Dayton, Ohio
Alma mater	[[College of the Holy Cross (Worcester, Massachusetts)[University of California, Berkeley]]
Known for	Clemens conjecture
Awards	Sloan Research Fellowship Invited Speaker, International Congress of Mathematicians (1974, 1986)
Scientific career
Fields	Mathematics
Institutions	Columbia University University of Utah
Thesis	Picard-Lefschetz Theorem for Families of Algebraic Varieties Acquiring Certain Singularities  (1966)
Doctoral advisor	Phillip Griffiths
Doctoral students	Enrico Arbarello

Charles Herbert Clemens Jr., known as Herbert Clemens, (born 15 August 1939 in Dayton, Ohio) is an American mathematician, specializing in complex algebraic geometry.

Biography

Clemens received in 1961 his bachelor's degree from Holy Cross College and in 1966 his Ph.D. from the University of California, Berkeley under Phillip Griffiths with thesis Picard-Lefschetz Theorem for Families of Algebraic Varieties Acquiring Certain Singularities. He became at Columbia University in 1970 an assistant professor and then an associate professor before leaving to become in 1975 an associate professor at the University of Utah, where he became a full professor in 1976.

Clemens was a visiting scholar at the Institute for Advanced Study from September 1968 to March 1970 and from September 2001 to June 2003. He was an invited speaker at the International Congress of Mathematicians in 1976 at Vancouver and in 1986 at Berkeley and gave a talk Curves on higher dimensional complex projective manifolds. For the academic year 1974–1975 he was a Sloan Fellow.

In 1972 Clemens and Griffiths proved that a cubic three-fold is in general not a rational variety, providing an example for three dimensions that unirationality does not imply rationality. In 1986 Clemens was an editor of the Pacific Journal of Mathematics.

He married in 1983 and has three children.

Selected publications

Articles

• "Picard-Lefschetz theorem for families of nonsingular algebraic varieties acquiring ordinary singularities". Trans. Amer. Math. Soc. 136: 93–108. 1969. doi:10.1090/s0002-9947-1969-0233814-9. MR 0233814.
• with Phillip Griffiths: "The Intermediate Jacobian of the Cubic Threefold". Annals of Mathematics. 95: 281–356. 1972. doi:10.2307/1970801. JSTOR 1970801.
• "Homological equivalence modulo algebraic equivalence is not finitely generated" (PDF). Publications Mathématiques de l'IHÉS. 58: 19–38. 1983. doi:10.1007/bf02953771.
• "Curves on generic hypersurfaces" (PDF). Annales Scientifiques de l'École Normale Supérieure. 19 (4): 629–636. 1986.

Books

• A scrapbook of complex curve theory. Plenum Press. 1980.
• as editor with: János Kollár: Current topics in complex algebraic geometry. Cambridge UP. 1995.
• with Michael A. Clemens: Geometry for the class room, Springer 1991
• as editor with Spencer Bloch and others: Algebraic Geometry: Bowdoin 1985, 2 vols., AMS 1987; Part 1. Part 2.
• as co-contributor with Alessio Corti to the book authored by János Kollár, and Shigefumi Mori: Birational geometry of algebraic varieties, Cambridge UP 1998.

External links

• website of C. Herbert Clemens at the University of Utah