Chadmark L. Schoen
- Professor of Mathematics
Monday 11-12 and tuesday 11-12
or by appointment
Research Areas and Keywords
Geometry: Differential & Algebraic
algebraic cycles, Chow groups, Hodge conjecture, Tate conjecture, Generalized Birch and Swinnerton-Dywer conjecture, algebraic surfaces, algebraic threefolds, varieties over finite fields, Galois representations and cohomology
I work on the geometry and arithmetic of figures defined by polynomial equations. I am especially interested in the geometry of algebraic curves, surfaces, threefolds and fourfolds over the complex numbers, over numbers fields, over finite fields, over fields of transcendence degree one over finite fields and over discrete valuation rings with perfect residue field. More specifically I study elliptic surfaces, elliptic threefolds, Calabi-Yau varieties, abelian varieties and surfaces of general type. I am interested in Chow groups of algebraic varieties and the relationship between a variety's Chow groups and its arithmetic and geometric properties.
Selected Grants
Chow Groups of Projective Varieties awarded by National Science Foundation (Principal Investigator). 2002 to 2006
Chow Groups of Smooth Projective Varieties awarded by National Science Foundation (Principal Investigator). 1999 to 2003
Mathematical Sciences: Chow Groups of Smooth Projective Varieties awarded by National Science Foundation (Principal Investigator). 1993 to 1996
Chow Groups of Smooth Projective Varieties awarded by National Science Foundation (Principal Investigator). 1993 to 1994
Chow Groups of Smooth Projective Varieties awarded by National Science Foundation (Principal Investigator). 1991 to 1992
Schoen, C. “On certain complex projective manifolds with Hodge numbers H10 = 4 and h20 = 5.” Michigan Mathematical Journal, vol. 68, no. 3, Jan. 2019, pp. 565–96. Scopus, doi:10.1307/mmj/1562032917. Full Text
Schoen, Chad. “An arithmetic ball quotient surface whose Albanese variety is not of CM type.” Electronic Research Announcements in Mathematical Sciences, vol. 21, no. 0, American Institute of Mathematical Sciences (AIMS), Sept. 2014, pp. 132–36. Crossref, doi:10.3934/era.2014.21.132. Full Text
Schoen, C. “Torsion in the cohomology of desingularized fiber products of elliptic surfaces.” Michigan Mathematical Journal, vol. 62, no. 1, Mar. 2013, pp. 81–115. Scopus, doi:10.1307/mmj/1363958242. Full Text
Schoen, C. “The geometric genus of a desingularized fiber product of elliptic surfaces.” Proceedings of the American Mathematical Society, vol. 141, no. 3, Jan. 2013, pp. 745–52. Scopus, doi:10.1090/S0002-9939-2012-11426-1. Full Text
Schoen, C. “Desingularized fiber products of semi-stable elliptic surfaces with vanishing third Betti number.” Compositio Mathematica, vol. 145, no. 1, Jan. 2009, pp. 89–111. Scopus, doi:10.1112/S0010437X08003801. Full Text
Schoen, C. “A family of surfaces constructed from genus 2 curves.” International Journal of Mathematics, vol. 18, no. 5, May 2007, pp. 585–612. Scopus, doi:10.1142/S0129167X07004175. Full Text
Schoen, C., and J. Top. “Drinfeld modules and torsion in the Chow groups of certain threefolds.” Proceedings of the London Mathematical Society, vol. 95, no. 3, Jan. 2007, pp. 545–66. Scopus, doi:10.1112/plms/pdm013. Full Text
Schoen, C. “Fermat covers, fermat hypersurfaces and abelian varieties of fermat type.” Quarterly Journal of Mathematics, vol. 57, no. 4, Dec. 2006, pp. 539–54. Scopus, doi:10.1093/qmath/hal004. Full Text
Schoen, C. “Specialization of the torsion subgroup of the Chow group.” Mathematische Zeitschrift, vol. 252, no. 1, Jan. 2006, pp. 11–17. Scopus, doi:10.1007/s00209-005-0837-2. Full Text
Schoen, C. “Albanese standard and albanese exotic varieties.” Journal of the London Mathematical Society, vol. 74, no. 2, Jan. 2006, pp. 304–20. Scopus, doi:10.1112/S0024610706023076. Full Text
Pages
Schoen, C. “Invariants of regular models of the product of two elliptic curves at a place of multiplicative reduction.” Arithmetic and Geometry of K3 Surfaces and Calabi Yau Threefolds, vol. 67, Springer, 2013, pp. 461–87.
Schoen, C. “Cyclic covers of P^v branched along v+2 hyperplanes and the generalized Hodge conjecture for certain abelian varieties.” Arithmetic of Complex Manifolds, vol. 1399, Springer-Verlag, 1989, pp. 137–54.
Schoen, C. “Zero cycles modulo rational equivalence for some varieties over fields of transcendence degree one.” Algebraic Geometry, Bowdoin 1985, vol. 46 part 2, american mathematical society, pp. 463–74.
Schoen, C. L. “Cohomology computations related to the l-adic Abel-Jacobi map modulo l.” The Arithmetic and Geometry of Algebraic Cycles, vol. 548, pp. 433–66.
Six graduate students participated in the May 15, 2016 graduation ceremonies to celebrate earning their PhDs in Mathematics. Their thesis topics were impressive and varied, and reflected the breadth of study in the department. Their advisors and... read more »