# Chadmark L. Schoen

- Professor of Mathematics

**External address:**191 Physics Bldg, 120 Science Drive Box 90320, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2813

**Office Hours:**

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

(95-0609) Mathematical Sciences: Chow Groups of Smooth Projective Varieties awarded by National Science Foundation (Principal Investigator). 1993 to 1996

(94-0815) Mathematical Sciences: Chow Groups of Smooth Projective Varieties awarded by National Science Foundation (Principal Investigator). 1993 to 1995

(93-0410) Chow Groups of Smooth Projective Varieties awarded by National Science Foundation (Principal Investigator). 1993 to 1994

(90-0544) 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.
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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*, vol. 21, no. 0, American Institute of Mathematical Sciences (AIMS), Sept. 2014, pp. 132–36. *Crossref*, doi: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*, vol. 62, no. 1, Mar. 2013, pp. 81–115. *Scopus*, doi: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*, vol. 141, no. 3, Jan. 2013, pp. 745–52. *Scopus*, doi: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*, vol. 145, no. 1, Jan. 2009, pp. 89–111. *Scopus*, doi:10.1112/S0010437X08003801.
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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.
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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*, vol. 95, no. 3, Jan. 2007, pp. 545–66. *Scopus*, doi:10.1112/plms/pdm013.
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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.
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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.
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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.
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## 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 »