Chad 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 group and its arithmetic and geometric properties.

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

Teaching (Spring 2025):

MATH 602.01, COMMUTATIVE ALGEBRA Synopsis
Physics 205, MW 08:30 AM-09:45 AM
MATH 790-90.05, MINICOURSE IN ADVANCED TOPICS Synopsis
Physics 119, TuTh 10:05 AM-11:20 AM

Office Hours:: Monday 3:30-4:30 and Friday 4:00-5:00
or by appointment

Education:

Ph.D.	The 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
Humberto Diaz

Recent Publications

Schoen, C, HODGE NUMBERS OF DESINGULARIZED FIBER PRODUCTS OF ELLIPTIC SURFACES, Proceedings of the American Mathematical Society, vol. 152 no. 8 (August, 2024), pp. 3215-3228 [doi] [abs]
Beauville, A; Schoen, C, A Non-Hyperelliptic Curve with Torsion Ceresa Cycle Modulo Algebraic Equivalence, International Mathematics Research Notices, vol. 2023 no. 5 (March, 2023), pp. 3671-3675, Oxford University Press (OUP) [doi] [abs]
Schoen, C, On certain complex projective manifolds with Hodge numbers H¹⁰ = 4 and h²⁰ = 5, Michigan Mathematical Journal, vol. 68 no. 3 (January, 2019), pp. 565-596 [doi]
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]
Schoen, C, Torsion in the cohomology of desingularized fiber products of elliptic surfaces, Michigan Mathematical Journal, vol. 62 no. 1 (March, 2013), pp. 81-115, Michigan Mathematical Journal, ISSN 0026-2285 [doi]