We extend Orlov’s result on representability of equivalences to schemes projective over a field. We also investigate the quasi-projective case.

This paper constitutes a preliminary discussion of joint work in progress as presented by the first author at Stony Brook in June 1991 at the symposium in honor of John Milnor. Our results include a construction of an intersection pairing on spaces of algebraic cycles on a given smooth complex quasi-projective variety, thereby providing a ring structure in “Lawson homology.” We verify that the ...

We study the ideals of the rational cohomology ring of the Hilbert scheme X [n] of n points on a smooth projective surface X . As an application, for a large class of smooth quasi-projective surfaces X , we show that every cup product structure constant of H∗(X ) is independent of n; moreover, we obtain two sets of ring generators for the cohomology ring H∗(X ). Similar results are established ...

In this paper it is proved that the volumes of the moduli spaces of polarized Calabi-Yau manifolds with respect to Weil-Petersson metrics are rational numbers. Mumford introduce the notion of a good metric on vector bundle over a quasi-projective variety in [10]. He proved that the Chern forms of good metrics define classes of cohomology with integer coefficients on the compactified quasi-proje...

— We establish the correspondence between tame harmonic bundles and μL-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for μL-stable parabolic Higgs bundles. Then we show that any local system on a smooth quasi projective variety can be deformed to a variation of polarized Hodge structure. As a consequence, we can conclude ...

We define the concept of an affinized projective variety and show how one can, in principle, obtain q-identities by different ways of computing the Hilbert series of such a variety. We carry out this program for projective varieties associated to quadratic monomial ideals. The resulting identities have applications in describing systems of quasi-particles containing null-states and can be inter...

We define push-forwards along projective morphisms in the Witt theory of smooth quasi-projective varieties over a field. We prove that they have standard properties such as functoriality, compatibility with pull-backs and projection formulas.