Related papers: The logarithmic gauged linear sigma model

Witten's gauged linear sigma model [Wi1] is one of the universal frameworks or structures that lie behind stringy dualities. Its A-twisted moduli space at genus 0 case has been used in the Mirror Principle [L-L-Y] that relates Gromov-Witten…

We prove a closed formula for integrals of the cotangent line classes against the top Chern class of the Hodge bundle on the moduli space of stable pointed curves. These integrals are computed via relations obtained from virtual…

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

We construct relative Gromov--Witten theory with expanded degenerations in the normal crossings setting and establish a degeneration formula for the resulting invariants. Given a simple normal crossings pair $(X,D)$, we show that there…

Moduli spaces of stable maps to a smooth projective variety typically have several components. We express the virtual class of the moduli space of genus one stable maps to a smooth projective variety as a sum of virtual classes of the…

We construct Gromov-Witten invariants of general symplectic manifolds.

We investigate the surjectivity of the real cycle class map from $I$-cohomology to classical intergral cohomology for some real smooth varieties, in particular surfaces. This might be considered as one of several possible incarnations of…

This semi-expository paper discusses the log minimal model program as applied to the moduli space of curves, especially in the case of curves of genus two. Log canonical models for these moduli spaces can often be constructed using the…

A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…

We introduce the stack of r-spin maps. These are stable maps into a variety V from n-pointed algebraic curves of genus g, with the additional data of an r-spin structure on the curve. We prove that this stack is a Deligne-Mumford stack, and…

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…

The notion of $m/\Gamma$-pointed stable curves is introduced. It should be viewed as a generalization of the notion of m-pointed stable curves of a given genus, where the labels of the marked points are only determined up to the action of a…

We give a log-geometric description of the space of twisted canonical divisors constructed by Farkas--Pandharipande. In particular, we introduce the notion of a principal rubber $k$-log-canonical divisor, and we study its moduli space. It…

We study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of…

In general, a Kobayashi-Hitchin correspondence establishes an isomorphism between a moduli space of stable algebraic geometric objects and a moduli space of solutions of a certain (generalized) Hermite-Einstein equation. We believe that,…

We construct a proper moduli space which is a Deligne-Mumford stack parametrising quasimaps relative to a simple normal crossings divisor in any genus using logarithmic geometry. We show this moduli space admits a virtual fundamental class…

In this note, we give a formulation of log structures for derived stacks using Olsson's log stack. The derived cotangent complex is then Olsson's logarithmic cotangent complex, which (unlike Gabber's) is just given by log differential forms…

We prove that the moduli space of stable logarithmic maps with fixed numerical invariants, from logarithmic curves to a fixed projective target logarithmic scheme with fine and saturated logarithmic structure, is a proper algebraic stack.…

We proceed to study the hybrid integrable structure in two-dimensional non-linear sigma models with target space three-dimensional squashed spheres. A quantum affine algebra and a pair of Yangian algebras are realized in the sigma models…

robustloggamma is an R package for robust estimation and inference in the generalized loggamma model. We briefly introduce the model, the estimation procedures and the computational algorithms. Then, we illustrate the use of the package…