The characteristic polynomial of a monodromy transformation attached to a family of curves.
The cohomology ring of polygon spaces
We compute the integer cohomology rings of the “polygon spaces”introduced in [F. Kirwan, Cohomology rings of moduli spaces of vector bundles over Riemann surfaces, J. Amer. Math. Soc., 5 (1992), 853-906] and [M. Kapovich & J. Millson, the symplectic geometry of polygons in Euclidean space, J. of Diff. Geometry, 44 (1996), 479-513]. This is done by embedding them in certain toric varieties; the restriction map on cohomology is surjective and we calculate its kernel using ideas from the theory...
The Formal Hodge Filtration.
The Hodge Conjecture for a Certain Class of Fourfolds.
The hodge conjecture for cubic fourfolds
The homotopy axiom in semialgebraic cohomology.
The indecomposability of H*(G/B, L)
The local Torelli-theorem. II : cyclic branched coverings
The Monodromy of a Degenerating Family of Curves.
The Néron-Severi group and the mixed Hodge structure on H2.
Théorèmes de Lefschetz pour les lieux de dégénérescence
Topology of Affine Varieties Dominated by an Affine Space.
Topology of real algebraic T-surfaces.
The paper is devoted to algebraic surfaces which can be obtained using a simple combinatorial procedure called the T-construction. The class of T-surfaces is sufficiently rich: for example, we construct T-surfaces of an arbitrary degree in RP³ which are M-surfaces. We also present a construction of T-surfaces in RP³ with dim H1 (RX; Z/2) > h1, 1(CX), where RX and CX are the real and the complex point sets of the surface.
Twisted action of the symmetric group on the cohomology of a flag manifold
Classes dual to Schubert cycles constitute a basis on the cohomology ring of the flag manifold F, self-adjoint up to indexation with respect to the intersection form. Here, we study the bilinear form (X,Y) :=〈X·Y, c(F)〉 where X,Y are cocycles, c(F) is the total Chern class of F and〈,〉 is the intersection form. This form is related to a twisted action of the symmetric group of the cohomology ring, and to the degenerate affine Hecke algebra. We give a distinguished basis for this form, which is a...