Related papers: Cohomology of moduli spaces

We describe the Chow rings of moduli spaces of ordered configurations of points on the projective line for arbitrary (sufficiently generic) stabilities. As an application, we exhibit such a moduli space admitting two small…

We study the moduli stacks of real vector bundles of fixed rank and degree on a type I real algebraic curve and determine its mod 2 cohomology algebra in terms of characteristic classes.

We construct a new compactification of the moduli space H_g of smooth hyperelliptic curves of genus g. We compare our compactification with other well-known remarkable compactifications of H_g .

We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to $\#^{g}(S^{n+1}\times S^{n})$, provided $n \geq 4$. This is an odd dimensional analogue of a recent homological stability result of S. Galatius and…

This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the moduli space of stable algebraic curves and,…

We prove the genus zero part of the generalized Witten conjecture relating moduli spaces of spin curves to Gelfand-Dickey hierarchies. That is, we show that intersection numbers on the moduli space of stable r-spin curves assemble into a…

We compute the cohomology of the right generalised projective Stiefel manifolds and use it to find bounds on the rank of the complementary bundle for certain vector bundles. Further the cohomology computations are also used to find bounds…

We introduce coupled Seiberg-Witten equations, and we prove, using a generalized vortex equation, that, for Kaehler surfaces, the moduli space of solutions of these equations can be identified with a moduli space of holomorphic stable…

This thesis intends to make a contribution to the theories of algebraic cycles and moduli spaces over the real numbers. In the study of the subvarieties of a projective algebraic variety, smooth over the field of real numbers, the cycle…

We propose a new system of conjectural relations in the tautological ring of the moduli space of curves involving stable rooted trees with level structure decorated by Hodge and {\Omega}-classes and prove these conjectures in different…

We construct new "virtually smooth" modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties. They generalize Givental's compactifications, when the complex structure of the curve is allowed…

We determine the convergence regions of certain local integrals on the moduli spaces of curves in neighborhoods of fixed stable curves in terms of the combinatorics of the corresponding graphs.

We construct a moduli space of stable pairs over a smooth projective variety, parametrizing morphisms from a fixed coherent sheaf to a varying sheaf of fixed topological type, subject to a stability condition. This generalizes the notion…

Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point. Using this description of the local…

We observe a general structure theorem for quantum cohomology rings, a non-homogeneous version of the usual cohomology ring encoding information about (almost holomorphic) rational curves. An application is the rigorous computation of the…

We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…

We prove that the moduli of stable supercurves with punctures is a smooth proper DM stack and study an analog of the Mumford's isomorphism for its canonical line bundle.

We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber…

We produce an equality between the Gromov-Witten invariants of the moduli space M of rank two odd degree stable vector bundles over a Riemann surface $\Sigma$ and the Donaldson invariants of the algebraic surface $\Sigma \times P^1$. We…

Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…