Let c : C → X×X be a correspondence with C and X quasi-projective schemes over an algebraically closed field k. We show that if u` : c ∗ 1Q` → c2Q` is an action defined by the localized Chern classes of a c2-perfect complex of vector bundles on C, where ` is a prime invertible in k, then the local terms of u` are given by the class of an algebraic cycle independent of `. We also prove some rela...

In this paper we construct the Poincare line bundle for stack of Higgs bundles on smooth projective curves and show that it induces a fully-faithful Fourier-Mukai transform category quasi-coherent sheaves.

Mochizuki’s work on torally indigenous bundles [1] yields combinatorial identities by degenerating to different curves of the same genus. We rephrase these identities in combinatorial language and strengthen them, giving relations between Ehrhart quasi-polynomials of different polytopes. We then apply the theory of Ehrhart quasi-polynomials to conclude that the number of dormant torally indigen...

This paper presents an method of self-calibration of varying internal camera parameters that based on quasi-affine reconstruction. In a stratified approach to self-calibration, a projective reconstruction is obtained first and this is successively refined first to an affine and then to a Euclidean reconstruction. It has been observed that the difficult step is to obtain the affine reconstructio...

∇−good filtration dimensions of modules and of algebras are introduced by Parker for quasi-hereditary algebras. These concepts are now generalized to the setting of standardly stratified algebras. Let A be a standardly stratified algebra. The ∇-good filtration dimension of A is proved to be the projective dimension of the characteristic module of A. Several characterizations of ∇good filtration...

As was shown in [2], totally categorical structures (i.e. which are categorical in all powers) are not finitely axiomatizable. On the other hand, the most simple totally categorical structures: infinite sets, infinite projective or affine geometries over a finite field, are quasi finitely axiomatizable (i.e. axiomatized by a finite number of axioms and the schema of infinity, we will use the ab...

A finite simple graph Γ determines a right-angled Artin group GΓ, with one generator for each vertex v, and with one commutator relation vw = wv for each pair of vertices joined by an edge. The Bestvina-Brady group NΓ is the kernel of the projection GΓ → Z, which sends each generator v to 1. We establish precisely which graphs Γ give rise to quasi-Kähler (respectively, Kähler) groups NΓ. This y...

We prove a conjecture of Griffiths on the quasi-projectivity images period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop theory analytic spaces and coherent sheaves that are definable with respect to given structure, GAGA-type theorem algebraizing complex algebraic spaces. then combine this theorems Artin show proper algebraic. Applying maps, ...

We investigate int-amplified endomorphisms on normal projective surfaces. prove that the output of equivariant MMP is either a Q-abelian surface, (equivariant) quasi-étale quotient smooth Mori dream space, or cone an elliptic curve.

We construct virtual fundamental classes in all intersection theories including Chow theory, K-theory and algebraic cobordism for quasi-projective Deligne-Mumford stacks with perfect obstruction prove the pullback formula, torus localization formula cosection principle.