相关论文: Geometry of equivariant compactifications of $G^n_…

Fix a finite group $G$. We seek to classify varieties with $G$-action equivariantly birational to a representation of $G$ on affine or projective space. Our focus is odd-dimensional smooth complete intersections of two quadrics, relating…

We study the fixed points of the universal G-equivariant n-dimensional complex vector bundle and obtain a decomposition formula in terms of twisted equivariant universal complex vector bundles of smaller dimension. We use this decomposition…

For any compact Lie group $G$ and any $n$ we construct a smooth $G$-manifold $U_n(G)$ such that any smooth $n$-dimensional $G$-manifold can be embedded in $U_n(G)$ with a trivial normal bundle. Furthermore, we show that such embeddings are…

We use the techniques of birational algebraic geometry and some combinatorial arguments related to weighted trees to study the structure of resolutions of compactifications of hypothetical counterexamples to the two-dimensional Jacobian…

In the present paper, we study several complex manifolds by using the following idea. First, we construct a certain moduli space and study the fundamental group of this space. This fundamental group is naturally mapped to the groups…

This paper reviews results and techniques from the authors' previous work "Symplectomorphism group relations and degenerations of Landau-Ginzburg models" and applies them in basic examples. The main example is the $A_n$ category where we…

We study certain moduli spaces of sheaves on Enriques surfaces thereby obtaining, in every odd dimension, new examples of Calabi-Yau manifolds. We describe the geometry (canonical bundle, fundamental group, second Betti number and certain…

Let G be a connected reductive group and X an equivariant compactifiction of G. In X, we study generalised and opposite generalised Schubert varieties, their intersections called generalised Richardson varieties and projected generalised…

The equivariant cohomology of a space with a group action is not only a ring but also an algebra over the cohomology ring of the classifying space of the acting group. We prove that toric manifolds (i.e. compact smooth toric varieties) are…

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…

We construct a sequence of modular compactifications of the space of marked trigonal curves by allowing the branch points to coincide to a given extent. Beginning with the standard admissible cover compactification, the sequence first…

We determine the maximal dimension of compact subvarieties of $\mathcal{A}_g$, the moduli space of complex principally polarized abelian varieties of dimension $g$, and the maximal dimension of a compact subvariety through a very general…

We study the canonical complexifications of non-compact Riemannian symmetric spaces G/K by the Grauert tube construction. We determine the maximal such complexification, a domain already constructed in another context by Akhiezer and…

We classify $G$-Mori fibre spaces equivariantly birational to smooth quadric threefolds with fixed-point free actions of the alternating group $G=\mathfrak A_5$. We deduce that such quadric threefolds are $G$-solid and the $G$-actions on…

Let G be a semisimple affine algebraic group and P a parabolic subgroup of G. We classify all flag varieties G/P which admit an action of the commutative unipotent group G_a^n with an open orbit.

In this paper we define a Poisson structure on some moduli spaces related to principal G-bundles on elliptic curves, the simplest example being the moduli space of stable pairs: a vector bundle and its global section. We also study…

We construct a combinatorial moduli space closely related to the KSV-compactification of the moduli space of bordered marked Riemann surfaces. The open part arises from symmetric metric ribbon graphs. The compactification is obtained by…

For Hamiltonian circle actions on compact, connected, four-dimensional manifolds, we give a generators and relations description for the even part of the equivariant cohomology, as an algebra over the equivariant cohomology of a point. This…

We describe a class of compact $G_2$ orbifolds constructed from non-symplectic involutions of K3 surfaces. Within this class, we identify a model for which there are infinitely many associative submanifolds contributing to the effective…

Let V be a representation space of a finite group G. We determine the group structure of the first homology of the equivariant diffeomorphism group of V. Then we can apply it to the calculation of the first homology of the corresponding…