Chadmark L. Schoen

Journal Article Proceedings of the American Mathematical Society · August 1, 2024 Each element of (Z≥0)2 is realized as the Hodge vector (h3,0(Z), h2,1(Z)) of some compact, connected, three dimensional, complex, submanifold, Z ⊂ PNC . Each (x, y) ∈ (Z≥1)2 with y ≤ 11x + 8 is shown to be the Hodge vector of a projective desingularized fi ... Full text Cite

A Non-Hyperelliptic Curve with Torsion Ceresa Cycle Modulo Algebraic Equivalence

Journal Article International Mathematics Research Notices · March 1, 2023 We exhibit a non-hyperelliptic curve C of genus 3 such that the class of the Ceresa cycle [C]-[C-] in JC modulo algebraic equivalence is torsion. ... Full text Cite

On certain complex projective manifolds with Hodge numbers H¹⁰ = 4 and h²⁰ = 5

Journal Article Michigan Mathematical Journal · January 1, 2019 Full text Cite

An arithmetic ball quotient surface whose Albanese variety is not of CM type

Journal Article Electronic Research Announcements in Mathematical Sciences · September 2014 Full text Cite

Torsion in the cohomology of desingularized fiber products of elliptic surfaces

Journal Article Michigan Mathematical Journal · March 1, 2013 Full text Cite

The geometric genus of a desingularized fiber product of elliptic surfaces

Journal Article Proceedings of the American Mathematical Society · January 3, 2013 A formula for the geometric genus is given under the assumption of tame ramification. © 2012, American Mathematical Society. ... Full text Cite

Invariants of regular models of the product of two elliptic curves at a place of multiplicative reduction

Other Arithmetic and geometry of K3 surfaces and Calabi-Yau threefolds · 2013 Cite

Desingularized fiber products of semi-stable elliptic surfaces with vanishing third Betti number

Journal Article Compositio Mathematica · January 1, 2009 Desingularized fiber products of semi-stable elliptic surfaces with Hetale3etale = 0 are classified. Such varieties may play a role in the study of supersingular threefolds, of the deformation theory of varieties with trivial canonical bundle, and of arith ... Full text Cite

A family of surfaces constructed from genus 2 curves

Journal Article International Journal of Mathematics · May 1, 2007 We consider the deformations of the two-dimensional complex analytic variety constructed from a genus 2 Riemann surface by attaching its self-product to its Jacobian in an elementary way. The deformations are shown to be unobstructed, the variety smooths t ... Full text Cite

Drinfeld modules and torsion in the Chow groups of certain threefolds

Journal Article Proceedings of the London Mathematical Society · January 1, 2007 Let E → B be an elliptic surface defined over the algebraic closure of a finite field of characteristic greater than 5. Let W be a resolution of singularities of E × B E. We show that the l-adic Abel-Jacobi map from the l-power-torsion in the second Chow g ... Full text Cite

Fermat covers, fermat hypersurfaces and abelian varieties of fermat type

Journal Article Quarterly Journal of Mathematics · December 1, 2006 Albanese maps for smooth projective models of a class of Abelian covers of projective space branched along particular hyperplane arrangements are studied. In some cases it is shown that the image of the Albanese map gives a cycle in the Albanese variety wh ... Full text Cite

Specialization of the torsion subgroup of the Chow group

Journal Article Mathematische Zeitschrift · January 1, 2006 An example is given in which specialization is not injective. © Springer-Verlag 2005. ... Full text Cite

Albanese standard and albanese exotic varieties

Journal Article Journal of the London Mathematical Society · January 1, 2006 Smooth complete algebraic varieties defined over an algebraically closed field are divided into two classes according to the behaviour of the albanese map. Criteria are given for when a variety belongs to either class. The relationship with the Tate conjec ... Full text Cite

complex varieties for which the chow group mod n is not finite

Journal Article Journal of Algebraic Geometry · January 1, 2002 Using the recent work of S. Bloch and H. Esnault, we give examples of smooth projective varieties W/ℚ and integers n ≠ 0 for which CH2(Wℚ)/nCH2(Wℚ) is not a finite group. ... Full text Cite

Cohomology computations related to the l-adic Abel-Jacobi map modulo l

Other The Arithmetic and Geometry of Algebraic Cycles · 2000 Cite

The Chow group modulo $l$ for the triple product of a general elliptic curve

Journal Article Asian Journal of Mathematics · 2000 Full text Cite

On certain exterior product maps of Chow groups

Journal Article Mathematical Research Letters · January 1, 2000 Full text Cite

On the image of the l-adic Abel-Jacobi map for a variety over the algebraic closure of a finite field

Journal Article Journal of the American Mathematical Society · January 1, 1999 Full text Cite

Addendum to: Hodge classes on self-products of a variety with an automorphism

Journal Article Compositio Mathematica · December 1, 1998 There are infinitely many fundamentally distinct families of polarized Abelian fourfolds of Weil type with multiplication from the cyclotomic field of cube roots of unity. The Hodge conjecture is shown to hold at a sufficiently general fiber in any of thes ... Cite

An integral analog of the Tate conjecture for one dimensional cycles on varieties over finite fields

Journal Article Mathematische Annalen · January 1, 1998 Full text Cite

Cycles, L-functions and triple products of elliptic curves

Journal Article Journal fur die Reine und Angewandte Mathematik · December 1, 1997 A variant of a conjecture of Beilinson and Bloch relates the rank of the Griffiths group of a smooth projective variety over a number field to the order of vanishing of an L-function at the center of the critical strip. Presently, there is little evidence ... Cite

Varieties dominated by product varieties

Journal Article International Journal of Mathematics · August 1, 1996 Full text Cite

The modified diagonal cycle on the triple product of a pointed curve

Journal Article Annales de l’institut Fourier · 1995 Full text Cite

On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field

Journal Article Ann. Sci. École Norm. Sup. · 1995 Cite

Stable quotients of periodic minimal surfaces

Journal Article Communications in Analysis and Geometry · 1994 Full text Cite

Complex multiplication cycles and a conjecture of beilinson and bloch

Journal Article Transactions of the American Mathematical Society · January 1, 1993 A generalization of the conjecture of Birch and Swinnerton-Dyer is investigated using complex multiplication cycles on a particular Kuga fiber variety. A weak finiteness result consistent with the conjecture is proved. The image of complex multiplication c ... Full text Cite

Chadmark L. Schoen

Selected Publications

HODGE NUMBERS OF DESINGULARIZED FIBER PRODUCTS OF ELLIPTIC SURFACES

A Non-Hyperelliptic Curve with Torsion Ceresa Cycle Modulo Algebraic Equivalence

On certain complex projective manifolds with Hodge numbers H¹⁰ = 4 and h²⁰ = 5

An arithmetic ball quotient surface whose Albanese variety is not of CM type

Torsion in the cohomology of desingularized fiber products of elliptic surfaces

The geometric genus of a desingularized fiber product of elliptic surfaces

Invariants of regular models of the product of two elliptic curves at a place of multiplicative reduction

Desingularized fiber products of semi-stable elliptic surfaces with vanishing third Betti number

A family of surfaces constructed from genus 2 curves

Drinfeld modules and torsion in the Chow groups of certain threefolds

Fermat covers, fermat hypersurfaces and abelian varieties of fermat type

Specialization of the torsion subgroup of the Chow group

Albanese standard and albanese exotic varieties

complex varieties for which the chow group mod n is not finite

Cohomology computations related to the l-adic Abel-Jacobi map modulo l

The Chow group modulo $l$ for the triple product of a general elliptic curve

On certain exterior product maps of Chow groups

On the image of the l-adic Abel-Jacobi map for a variety over the algebraic closure of a finite field

Addendum to: Hodge classes on self-products of a variety with an automorphism

An integral analog of the Tate conjecture for one dimensional cycles on varieties over finite fields

Cycles, L-functions and triple products of elliptic curves

Varieties dominated by product varieties

The modified diagonal cycle on the triple product of a pointed curve

On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field

Stable quotients of periodic minimal surfaces

Complex multiplication cycles and a conjecture of beilinson and bloch

On Hodge structures and nonrepresentability of Chow groups

Some examples of torsion in the Griffiths group

Produkte Abelscher Varietäten und Moduln Über Ordnungen

On certain modular representations in the cohomology of algebraic curves

Bounds for rational points on twists of constant hyperelliptic curves

Cyclic covers of P^v branched along v+2 hyperplanes and the generalized Hodge conjecture for certain abelian varieties

On fiber products of rational elliptic surfaces with section

Hodge classes on self-products of a variety with an automorphism

Zero cycles modulo rational equivalence for some varieties over fields of transcendence degree one

Complex multiplication cycles on elliptic modular threefolds

On the geometry of a special determinantal hypersurface associated to the Mumford-Horrocks vector bundle

Algebraic cycles on certain desingularized nodal hypersurfaces