Related papers: Virtual cycles of stable (quasi)-maps with fields

We prove that smooth, separated Deligne--Mumford stacks in mixed characteristic with quasi-projective coarse moduli space are global quotient stacks and satisfy the resolution property. This builds on work of Kresch and Vistoli and of…

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking…

In this paper, we give a proof of Hori's equation for intersection numbers of the moduli space of quasimaps from CP^{1} with (2+1) marked points to CP^{N-1} by using localization technique.

We show how a quasi-smooth derived enhancement of a Deligne-Mumford stack X naturally endows X with a functorial perfect obstruction theory in the sense of Behrend-Fantechi. This result is then applied to moduli of maps and perfect…

We show that moduli spaces of stable maps admits virtual orbifold structure. The symplectic version of virtual localization formula is obtained.

We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is naturally identified with the moduli space of extended tropical curves, and that this is compatible with the "naive" set-theoretic tropicalization…

We express nested Hilbert schemes of points and curves on a smooth projective surface as "virtual resolutions" of degeneracy loci of maps of vector bundles on smooth ambient spaces. We show how to modify the resulting obstruction theories…

We construct a smooth Deligne-Mumford compactification for the moduli space of curves with an m-tuple of spin structures using line bundles on quasi-stable curves as limiting objects, as opposed to line bundles on stacky curves. For all m,…

In this paper, we propose a definition of the moduli stack of stable relative ideal sheaves, and prove that it is a separated and proper Deligne-Mumford stack. It is the first part of the project of relative Donaldson-Thomas theory of ideal…

We study the Fulton-Macpherson operational Chow rings of good moduli spaces of properly stable, smooth, Artin stacks. Such spaces are \'etale locally isomorphic to geometric invariant theory quotients of affine schemes, and are therefore…

B. Kim and the first author proved a result comparing the virtual fundamental classes of the moduli spaces of stable quasimaps and stable LG-quasimaps by studying localized Chern characters for 2-periodic complexes. In this paper, we study…

In this paper we study quasi-symmetric conjugations of $C^2$ weakly order-preserving circle maps with a flat interval. Under the assumption that the maps have the same rotation number of bounded type and that bounded geometry holds we…

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…

In this paper, we define $\Lambda$-quot-functors on Deligne-Mumford stacks. We prove that the $\Lambda$-quot-functor is representable by an algebraic space. Then, we construct the moduli space of $\Lambda$-modules on a projective…

This informal note collects key results and open problems on the (co)homology of the Deligne-Mumford moduli spaces of real marked rational curves. The open problems are both of topological nature, aiming to investigate the (co)homology of…

Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection…

The main result of this paper amounts to a complete evaluation of the integral cohomological structure of the stable mapping class group. In particular it verifies the conjecture of D.Mumford about the rational cohomology of the stable…

We compute syntomic cohomology of semistable affinoids in terms of cohomology of $(\varphi,\Gamma)$-modules which, thanks to work of Fontaine-Herr, Andreatta-Iovita, and Kedlaya-Liu, is known to compute Galois cohomology of these affinoids.…

For $Y \subset X$ a locally complete intersection of codimension p, Spencer Bloch [2] constructed the semi-regularity map $\pi: H^{1}(\mathcal{N}_{Y/X}) \to H^{p+1}(\Omega_{X/k}^{p-1})$. As an analogue, we construct a map $\tilde{\pi}:…

Let $\mathcal{X}$ be a tame proper Deligne-Mumford stack of the form $[M/G]$ where $M$ is a scheme and $G$ is an algebraic group. We prove that the stack $\mathcal{K}_{g,n}(\mathcal{X},d)$ of twisted stable maps is a quotient stack and can…