Let n = (n1, . . . , nr). The quotient space Pn := S n1× · · ·×Snr/(x ∼ −x) is what we call a projective product space. We determine the integral cohomology ring H∗(Pn) and the action of the Steenrod algebra on H∗(Pn;Z2). We give a splitting of ΣPn in terms of stunted real projective spaces, and determine the ring K∗(Pn). We relate the immersion dimension and span of Pn to the much-studied sect...

0. Algebraic background 1. Projective sets and their ideals; Weak Nullstellensatz 2. Irreducible components 3. Hilbert polynomial. Nullstellensatz 4. Graded modules; resolutions and primary decomposition 5. Dimension, degree and arithmetic genus 6. Product of varieties 7. Regular maps 8. Properties of morphisms 9. Resolutions and dimension 10. Ruled varieties 11. Tangent spaces and cones; smoot...

We study stacks of slope-semistable twisted sheaves on orbisurfaces with projective coarse spaces and prove that in certain cases they have many of the asymptotic properties enjoyed by the moduli of slope-semistable sheaves on smooth projective surfaces.

The weight hierarchies and generalized weight spectra of the projective codes from degenerate quadrics in projective spaces over finite fields are determined. These codes satisfy also the chain conditions.

We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give a purely algebro-geometric proof of the projective reconstruction theorem by Hartley and Schaffalitzky [HS09].

We study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group. We apply these results to obtain qualitative results on real and complex hyperbolic spaces in 2 and 4 dimensions, related to generalizations of the Bethe-Sommerfeld conjecture and the Ten Martini Problem, ...

On a generic defining function of projective motion in the rigid 6-dimensional h-spaces 1 Zolfira Zakirova 2 Abstract In this note we find a generic defining function of projective motion in the 6-dimensional rigid h-space.

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical examples are Rn, Cn, (separable) Hilbert space and more generally all separable Banach spaces, the Cantor space 2N, the Baire space NN, the infinite symmetric group S∞...