Chadmark L. Schoen | Scholars@Duke

Chadmark L. Schoen
Professor of Mathematics

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.

Current Research Interests

Algebraic Geometry and some related areas of complex analytic geometry and number theory.

Office Hours

Monday 11-12 and Friday 11-12
or by appointment

Current Appointments & Affiliations

Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 1998

Contact Information

191 Physics Bldg, Durham, NC 27708
Box 90320, Durham, NC 27708-0320
schoen@math.duke.edu (919) 660-2813
http://www.math.duke.edu/~schoen

Background
Education, Training, & Certifications
- Ph.D., University of Chicago 1982
- B.A., Haverford College 1975
Duke Appointment History
- Director of Undergraduate Studies in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2013 - 2015
- Associate Professor with Tenure, Mathematics, Trinity College of Arts & Sciences 1991 - 1998
- Assistant Professor, Mathematics, Trinity College of Arts & Sciences 1982 - 1991
Recognition
Awards & Honors
- Collaboration Grants for Mathematicians. Simons Foundation. 2013
Research
Selected Grants
- Chow Groups of Projective Varieties awarded by National Science Foundation 2002 - 2006
- Chow Groups of Smooth Projective Varieties awarded by National Science Foundation 1999 - 2003
- (95-0609) Mathematical Sciences: Chow Groups of Smooth Projective Varieties awarded by National Science Foundation 1993 - 1996
- (94-0815) Mathematical Sciences: Chow Groups of Smooth Projective Varieties awarded by National Science Foundation 1993 - 1995
- (93-0410) Chow Groups of Smooth Projective Varieties awarded by National Science Foundation 1993 - 1994
- (90-0544) Chow Groups of Smooth Projective Varieties awarded by National Science Foundation 1991 - 1992
Publications & Artistic Works
Selected Publications
- Journal Articles
  - Schoen, C. "An arithmetic ball quotient surface whose Albanese variety is not of CM type." Electronic Research Announcements in Mathematical Sciences 21, no. 0 (September 2014): 132-136. Full Text
  - Schoen, C. "The geometric genus of a desingularized fiber product of elliptic surfaces." Proceedings of the American Mathematical Society 141, no. 3 (2013): 745-752. Full Text
  - Schoen, C. "Torsion in the cohomology of desingularized fiber products of elliptic surfaces." Michigan Mathematical Journal 62, no. 1 (2013): 81-115. Full Text
  - Schoen, C. "Desingularized fiber products of semi-stable elliptic surfaces with vanishing third Betti number." Compositio Mathematica 145, no. 1 (2009): 89-111. Full Text
  - Schoen, C, and Top, J. "Drinfeld modules and torsion in the Chow groups of certain threefolds." Proceedings of the London Mathematical Society 95, no. 3 (2007): 545-566. Full Text
  - Schoen, C. "A family of surfaces constructed from genus 2 curves." International Journal of Mathematics 18, no. 5 (2007): 585-612. Full Text
  - Schoen, C. "Specialization of the torsion subgroup of the Chow group." Mathematische Zeitschrift 252, no. 1 (2006): 11-17. Full Text
  - Schoen, C. "Albanese standard and albanese exotic varieties." Journal of the London Mathematical Society 74, no. 2 (2006): 304-320. Full Text
  - Schoen, C. "Fermat covers, fermat hypersurfaces and abelian varieties of fermat type." Quarterly Journal of Mathematics 57, no. 4 (2006): 539-554. Full Text
  - Schoen, C. "complex varieties for which the chow group mod n is not finite." Journal of Algebraic Geometry 11, no. 1 (2002): 41-100.
  - Schoen, C. "The Chow group modulo $l$ for the triple product of a general elliptic curve." Asian Journal of Mathematics 4, no. 4 (2000): 987-996. Full Text
  - Schoen, C. "On certain exterior product maps of Chow groups." Mathematical Research Letters 7, no. 2-3 (2000): 177-194.
  - Schoen, C. "On the image of the l-adic Abel-Jacobi map for a variety over the algebraic closure of a finite field." Journal of the American Mathematical Society 12, no. 3 (1999): 795-838.
  - Schoen, C. "An integral analog of the Tate conjecture for one dimensional cycles on varieties over finite fields." Mathematische Annalen 311, no. 3 (1998): 493-500.
  - Schoen, C. "Addendum to: Hodge classes on self-products of a variety with an automorphism." Compositio Mathematica 114, no. 3 (1998): 329-336.
  - Buhler, J, Schoen, C, and Top, J. "Cycles, L-functions and triple products of elliptic curves." Journal fur die Reine und Angewandte Mathematik 492 (1997): 93-133.
  - Schoen, C. "Varieties dominated by product varieties." International Journal of Mathematics 7, no. 4 (1996): 541-571. Full Text
  - Gross, BH, and Schoen, C. "The modified diagonal cycle on the triple product of a pointed curve." Annales de l’institut Fourier 45, no. 3 (1995): 649-679. Full Text
  - Schoen, C. "On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field." Ann. Sci. École Norm. Sup. 28, no. 4 (1995): 1-50.
  - Ross, M, and Schoen, C. "Stable quotients of periodic minimal surfaces." Communications in Analysis and Geometry 2, no. 3 (1994): 451-459. Full Text
  - Schoen, C. "Complex multiplication cycles and a conjecture of Beĭlinson and Bloch." Transactions of the American Mathematical Society 339, no. 1 (January 1, 1993): 87-115. Full Text
  - Schoen, C. "On Hodge structures and nonrepresentability of Chow groups." Compositio Math. 88 (1993): 285-316.
  - "Produkte Abelscher Varietäten und Moduln über Ordnungen." Journal für die reine und angewandte Mathematik (Crelles Journal) 1992, no. 429 (1992). Full Text
  - Schoen, C. "Some examples of torsion in the Griffiths group." Mathematische Annalen 293, no. 1 (1992): 651-679. Full Text
  - "Bounds for rational points on twists of constant hyperelliptic curves." Journal für die reine und angewandte Mathematik (Crelles Journal) 1990, no. 411 (1990). Full Text
  - Schoen, C. "On certain modular representations in the cohomology of algebraic curves." Journal of Algebra 135, no. 1 (1990): 1-18.
  - Schoen, C. "Hodge classes on self-products of a variety with an automorphism." Compositio Mathematica 65 (1988): 3-32.
  - Schoen, C. "On fiber products of rational elliptic surfaces with section." Mathematische Zeitschrift 197, no. 2 (1988): 177-199. Full Text
  - Schoen, C. "Complex multiplication cycles on elliptic modular threefolds." Duke Mathematical Journal 53, no. 3 (September 1986): 771-794. Full Text
  - "On the geometry of a special determinantal hypersurface associated to the Mumford-Horrocks vector bundle." Journal für die reine und angewandte Mathematik (Crelles Journal) 1986, no. 364 (1986). Full Text
  - Schoen, C. "Algebraic cycles on certain desingularized nodal hypersurfaces." Mathematische Annalen 270, no. 1 (1985): 17-27. Full Text
- Other Articles
  - 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 67 (2013): 461-487.
  - 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 1399 (1989): 137-154.
  - Schoen, C. "Zero cycles modulo rational equivalence for some varieties over fields of transcendence degree one." Algebraic Geometry, Bowdoin 1985 46 part 2: 463-474.
  - Schoen, CL. "Cohomology computations related to the l-adic Abel-Jacobi map modulo l." The Arithmetic and Geometry of Algebraic Cycles 548: 433-466.
Teaching & Mentoring
Recent Courses

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Education, Training, & Certifications

Duke Appointment History

Awards & Honors

Selected Grants

Selected Publications

Journal Articles

Other Articles

Recent Courses