Chadmark L. Schoen, Professor

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.

Contact Info:

Office Location:	191 Physics Bldg, 120 Science Drive Box 90320, Durham, NC 27708
Office Phone:	(919) 660-2813
Email Address:
Web Page:	http://www.math.duke.edu/~schoen

Teaching (Fall 2019):

• MATH 601.01, GROUPS, RINGS, AND FIELDS Synopsis

  Physics 205, WF 08:30 AM-09:45 AM

• MATH 502.01, ALGEBRAIC STRUCTURES II Synopsis

  Physics 205, WF 10:05 AM-11:20 AM

Office Hours:

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

Education:

Ph.D.	University of Chicago	1982
B.A.	Haverford College	1975

Specialties:

Algebra
Geometry

Research Interests: Algebraic Geometry

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.

Areas of Interest:

Geometry of algebraic varieties
Algebraic Cycles
Chow Groups

Keywords:

Algebraic geometry

Current Ph.D. Students   (Former Students)

• Humberto Diaz  

Recent Publications   (More Publications)

1. Schoen, C, On certain complex projective manifolds with Hodge numbers H¹⁰ = 4 and h²⁰ = 5, The Michigan Mathematical Journal, vol. 68 no. 3 (January, 2019), pp. 565-596 [doi]
2. Schoen, C, An arithmetic ball quotient surface whose Albanese variety is not of CM type, Electronic Research Announcements in Mathematical Sciences, vol. 21 (September, 2014), pp. 132-136, American Institute of Mathematical Sciences (AIMS) [doi]
3. Schoen, C, Torsion in the cohomology of desingularized fiber products of elliptic surfaces, The Michigan Mathematical Journal, vol. 62 no. 1 (March, 2013), pp. 81-115, Michigan Mathematical Journal, ISSN 0026-2285 [doi]
4. Schoen, C, The geometric genus of a desingularized fiber product of elliptic surfaces, Proceedings of the American Mathematical Society, vol. 141 no. 3 (January, 2013), pp. 745-752, American Mathematical Society (AMS), ISSN 0002-9939 [doi]  [abs]
5. Schoen, C, Invariants of regular models of the product of two elliptic curves at a place of multiplicative reduction, in Arithmetic and Geometry of K3 surfaces and Calabi-Yau Threefolds, Fields Institute Communications 67, edited by Laza, R. ; Schuett, M; and Yui, N., Arithmetic and Geometry of K3 Surfaces and Calabi Yau Threefolds, vol. 67 (2013), pp. 461-487, SPRINGER, ISBN 978-1-4614-6402-0