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 tuesday 11-12
or by appointment

Current Appointments & Affiliations

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

Contact Information

191 Physics Bldg, 120 Science Drive Box 90320, 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
- Director of Undergraduate Studies for the Department of Mathematics, Mathematics, Duke University 2012 - 2013
- Director of Undergraduate Studies for the Department of Mathematics, Mathematics, Duke University 2010 - 2012
- Ph.D., The 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
Expertise
Subject Headings
- Algebraic geometry
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
- Mathematical Sciences: Chow Groups of Smooth Projective Varieties awarded by National Science Foundation 1993 - 1996
- Chow Groups of Smooth Projective Varieties awarded by National Science Foundation 1993 - 1994
- Chow Groups of Smooth Projective Varieties awarded by National Science Foundation 1991 - 1992
Publications & Artistic Works
Selected Publications
- Academic Articles
  - Schoen, C. “On certain complex projective manifolds with Hodge numbers H¹⁰ = 4 and h²⁰ = 5.” Michigan Mathematical Journal 68, no. 3 (January 1, 2019): 565–96. https://doi.org/10.1307/mmj/1562032917.
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  - Schoen, Chad. “An arithmetic ball quotient surface whose Albanese variety is not of CM type.” Electronic Research Announcements in Mathematical Sciences 21, no. 0 (September 2014): 132–36. https://doi.org/10.3934/era.2014.21.132.
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  - Schoen, C. “Torsion in the cohomology of desingularized fiber products of elliptic surfaces.” Michigan Mathematical Journal 62, no. 1 (March 1, 2013): 81–115. https://doi.org/10.1307/mmj/1363958242.
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  - Schoen, C. “The geometric genus of a desingularized fiber product of elliptic surfaces.” Proceedings of the American Mathematical Society 141, no. 3 (January 3, 2013): 745–52. https://doi.org/10.1090/S0002-9939-2012-11426-1.
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  - Schoen, C. “Desingularized fiber products of semi-stable elliptic surfaces with vanishing third Betti number.” Compositio Mathematica 145, no. 1 (January 1, 2009): 89–111. https://doi.org/10.1112/S0010437X08003801.
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  - Schoen, C. “A family of surfaces constructed from genus 2 curves.” International Journal of Mathematics 18, no. 5 (May 1, 2007): 585–612. https://doi.org/10.1142/S0129167X07004175.
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  - Schoen, C., and J. Top. “Drinfeld modules and torsion in the Chow groups of certain threefolds.” Proceedings of the London Mathematical Society 95, no. 3 (January 1, 2007): 545–66. https://doi.org/10.1112/plms/pdm013.
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  - Schoen, C. “Fermat covers, fermat hypersurfaces and abelian varieties of fermat type.” Quarterly Journal of Mathematics 57, no. 4 (December 1, 2006): 539–54. https://doi.org/10.1093/qmath/hal004.
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  - Schoen, C. “Specialization of the torsion subgroup of the Chow group.” Mathematische Zeitschrift 252, no. 1 (January 1, 2006): 11–17. https://doi.org/10.1007/s00209-005-0837-2.
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  - Schoen, C. “Albanese standard and albanese exotic varieties.” Journal of the London Mathematical Society 74, no. 2 (January 1, 2006): 304–20. https://doi.org/10.1112/S0024610706023076.
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  - Schoen, C. “complex varieties for which the chow group mod n is not finite.” Journal of Algebraic Geometry 11, no. 1 (January 1, 2002): 41–100. https://doi.org/10.1090/S1056-3911-01-00291-0.
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  - Schoen, C. “On certain exterior product maps of Chow groups.” Mathematical Research Letters 7, no. 2–3 (January 1, 2000): 177–94. https://doi.org/10.4310/MRL.2000.v7.n2.a4.
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  - Schoen, Chad. “The Chow group modulo $l$ for the triple product of a general elliptic curve.” Asian Journal of Mathematics 4, no. 4 (2000): 987–96. https://doi.org/10.4310/ajm.2000.v4.n4.a15.
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  - 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 (January 1, 1999): 795–838. https://doi.org/10.1090/s0894-0347-99-00303-3.
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  - Schoen, C. “Addendum to: Hodge classes on self-products of a variety with an automorphism.” Compositio Mathematica 114, no. 3 (December 1, 1998): 329–36.
  - Schoen, C. “An integral analog of the Tate conjecture for one dimensional cycles on varieties over finite fields.” Mathematische Annalen 311, no. 3 (January 1, 1998): 493–500. https://doi.org/10.1007/s002080050197.
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  - Buhler, J., C. Schoen, and J. Top. “Cycles, L-functions and triple products of elliptic curves.” Journal Fur Die Reine Und Angewandte Mathematik 492 (December 1, 1997): 93–133.
  - Schoen, C. “Varieties dominated by product varieties.” International Journal of Mathematics 7, no. 4 (August 1, 1996): 541–71. https://doi.org/10.1142/S0129167X9600030X.
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  - Gross, Benedict H., and Chad Schoen. “The modified diagonal cycle on the triple product of a pointed curve.” Annales De L’Institut Fourier 45, no. 3 (1995): 649–79. https://doi.org/10.5802/aif.1469.
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  - 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, Marty, and Chad Schoen. “Stable quotients of periodic minimal surfaces.” Communications in Analysis and Geometry 2, no. 3 (1994): 451–59. https://doi.org/10.4310/cag.1994.v2.n3.a4.
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  - Schoen, C. “Complex multiplication cycles and a conjecture of beilinson and bloch.” Transactions of the American Mathematical Society 339, no. 1 (January 1, 1993): 87–115. https://doi.org/10.1090/S0002-9947-1993-1107030-6.
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  - Schoen, C. “On Hodge structures and nonrepresentability of Chow groups.” Compositio Math. 88 (1993): 285–316.
  - Schoen, C. “Some examples of torsion in the Griffiths group.” Mathematische Annalen 293, no. 1 (December 1, 1992): 651–79. https://doi.org/10.1007/BF01444739.
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  - Schoen, C. “Produkte Abelscher Varietäten und Moduln Über Ordnungen.” Journal Fur Die Reine Und Angewandte Mathematik 1992, no. 429 (January 1, 1992): 115–24. https://doi.org/10.1515/crll.1992.429.115.
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  - Schoen, C. “On certain modular representations in the cohomology of algebraic curves.” Journal of Algebra 135, no. 1 (November 15, 1990): 1–18. https://doi.org/10.1016/0021-8693(90)90147-G.
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  - Schoen, C. “Bounds for rational points on twists of constant hyperelliptic curves.” Journal Fur Die Reine Und Angewandte Mathematik 1990, no. 411 (January 1, 1990): 196–204. https://doi.org/10.1515/crll.1990.411.196.
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  - Schoen, C. “On fiber products of rational elliptic surfaces with section.” Mathematische Zeitschrift 197, no. 2 (June 1, 1988): 177–99. https://doi.org/10.1007/BF01215188.
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  - Schoen, C. “Hodge classes on self-products of a variety with an automorphism.” Compositio Mathematica 65 (1988): 3–32.
  - Schoen, C. “Complex multiplication cycles on elliptic modular threefolds.” Duke Mathematical Journal 53, no. 3 (September 1986): 771–94. https://doi.org/10.1215/S0012-7094-86-05343-3.
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  - Schoen, C. “On the geometry of a special determinantal hypersurface associated to the Mumford-Horrocks vector bundle.” Journal Fur Die Reine Und Angewandte Mathematik 1986, no. 364 (January 1, 1986): 85–111. https://doi.org/10.1515/crll.1986.364.85.
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  - Schoen, C. “Algebraic cycles on certain desingularized nodal hypersurfaces.” Mathematische Annalen 270, no. 1 (March 1, 1985): 17–27. https://doi.org/10.1007/BF01455524.
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- 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. Springer, 2013.
  - 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. Springer-Verlag, 1989.
  - Schoen, C. L. “Cohomology computations related to the l-adic Abel-Jacobi map modulo l.” The Arithmetic and Geometry of Algebraic Cycles, n.d.
  - Schoen, C. “Zero cycles modulo rational equivalence for some varieties over fields of transcendence degree one.” Algebraic Geometry, Bowdoin 1985. american mathematical society, n.d.
Teaching & Mentoring
Recent Courses
- MATH 502: Introduction to Algebraic Structures II 2020
- MATH 601: Groups, Rings, and Fields 2020
- MATH 790-90: Minicourse in Advanced Topics 2020
- MATH 601: Groups, Rings, and Fields 2019
- MATH 627: Algebraic Geometry 2019
- MATH 790-90: Minicourse in Advanced Topics 2019
- MATH 601: Groups, Rings, and Fields 2018

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Education, Training, & Certifications

Duke Appointment History

Awards & Honors

Subject Headings

Selected Grants

Selected Publications

Academic Articles

Other Articles

Recent Courses