Journal articleProceedings 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< ...
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Journal articleInternational 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. ...
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Journal articleCompositio 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 canonica ...
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Journal articleInternational 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 ...
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Journal articleProceedings 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 ...
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Journal articleQuarterly 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 ...
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Journal articleJournal 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 ...
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Journal articleJournal 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. ...
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Journal articleCompositio 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 ...
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Journal articleJournal 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 ...
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Journal articleTransactions 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 ...
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