A divisorial cycle acquiring an embedded component under a flat specialization
A geometric application of Nori’s connectivity theorem
We study (rational) sweeping out of general hypersurfaces by varieties having small moduli spaces. As a consequence, we show that general -trivial hypersurfaces are not rationally swept out by abelian varieties of dimension at least two. As a corollary, we show that Clemens’ conjecture on the finiteness of rational curves of given degree in a general quintic threefold, and Lang’s conjecture saying that such varieties should be rationally swept-out by abelian varieties, contradict.
A Lefschetz decomposition for Chow motives of abelian schemes.
A look into the Severi varieties of curves in higher codimension.
A minimal Set of Generators for the Ring of multisymmetric Functions
The purpose of this article is to give, for any (commutative) ring , an explicit minimal set of generators for the ring of multisymmetric functions as an -algebra. In characteristic zero, i.e. when is a -algebra, a minimal set of generators has been known since the 19th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving the degree bound previously...
A note on a theorem of Griffiths on the Abel-Jacobi map.
A note on indecomposable motivic cohomology classes.
A note on the cycle map.
A note on the Hilbert scheme of curves of degree and genus .
A priori bounds of Castelnuovo type for cohomological Hilbert functions.
A Remark on the Hilbert Scheme of smooth complex space curves.
A result on the integral chow ring of a generic principally polarized complex abelian variety of dimension four
A Smooth Four-Dimensional G-Hilbert Scheme
2000 Mathematics Subject Classification: 14C05, 14L30, 14E15, 14J35.When the cyclic group G of order 15 acts with some specific weights on affine four-dimensional space, the G-Hilbert scheme is a crepant resolution of the quotient A^4 / G. We give an explicit description of this resolution using G-graphs.
A Stratification of the Hilbert Scheme of Points in the Projective Plane.
A support theorem for Hilbert schemes of planar curves
Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the pushforward of the constant sheaf on the relative Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension. It follows that the perverse filtration on the cohomology of the compactified Jacobian of an integral plane curve...
A universal property of the Cayley-Chow space of algebraic cycles
Alexander duality in intersection theory
Algebraic cycles and infinite loop spaces.
Algebraic cycles, Chow varieties, and Lawson homology
Algebraic cycles on a general complete intersection of high multi-degree of a smooth projective variety