Related papers: Differential forms and smoothness of quotients by …

Given a smooth variety $X$ with an action of a finite group $G$, and a semiorthogonal decomposition of the derived category, $\mathcal{D}([X/G])$, of $G$-equivariant coherent sheaves on $X$ into subcategories equivalent to derived…

Let G be a compact Lie group acting transitively on Riemannian manifolds M and N. Let p be a G equivariant Riemannian submersion from M to N. We show that a smooth differential form on N has finite Fourier series if and only if the pull…

Let $X$ be a normal variety over a perfect field of positive characteristic and $B$ a reduced divisor on $X$. We prove that if the Cartier isomorphism on the log smooth locus of $(X,B)$ extends to the entire $X$, then $(X,B)$ satisfies the…

Let S be a Noetherian scheme, f:X->Y a surjective S-morphism of S-schemes, with X of finite type over S. We discuss what makes Y of finite type. First, we prove that if S is excellent, Y is reduced, and f is universally open, then Y is of…

Let G be a connected complex reductive group. A well known theorem of I. Losev's says that a smooth affine spherical G-variety X is uniquely determined by its weight monoid, which is the set of irreducible representations of G that occur in…

Let X be the quotient of a smooth projective variety over a field by a finite group action (in which case we say X is pseudo-smooth), such that the singularities of X are isolated k-rational points. Let Y be obtained by blowing up these…

In this note we consider a quotient \pi: X-> X/G, with G a finite group and X a smooth projective scheme such that X/G is smooth. We compare the equivariant derived category D^G(X) and the derived category of the quotient D(X/G) by giving…

We compute an upper bound for the dimension of the tangent spaces at classical points of certain eigenvarieties associated with definite unitary groups, especially including the so-called critically refined cases. Our bound is given in…

We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne-Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the so-called effective…

Let G be a connected reductive algebraic group over an algebraically closed field k. In a recent paper, Bate, Martin, R\"ohrle and Tange show that every (smooth) subgroup of G is separable provided that the characteristic of k is very good…

We give an explicit characterization of all principally polarized abelian varieties $(A,\Theta)$ such that there is a finite subgroup of automorphisms $G$ of $A$ that preserve the numerical class of $\Theta$, and such that the quotient…

We study relatively minimal surfaces equipped with a strongly isotrivial elliptic fibration in positive characteristic by means of the notion of equivariantly normal curves introduced and developed recently by Brion. Such surfaces are…

Let k be a field, and let {\pi}:\tilde{X} -> X be a proper birational morphism of irreducible k-varieties, where \tilde{X} is smooth and X has at worst quotient singularities. When the characteristic of k is zero, a theorem of Koll\'ar in…

Let $A$ be a complex torus and $G$ a finite group acting on $A$ without translations such that $A/G$ is smooth. Consider the subgroup $F\leq G$ generated by elements that have at least one fixed point. We prove that there exists a point…

In this paper we study the deformation and Q-Gorenstein deformation theory of schemes with non-isolated singularities. We obtain obstruction spaces for the existence of deformations and also for local deformations to exist globally. Finally…

Let $X$ be a smooth proper variety over an algebraically closed field of positive characteristic $p$. We find cohomological conditions for the Artin-Mazur formal group functors $\Phi^{i}(X,\mathbb{G}_m)$ to be formally smooth. We show that…

We consider the quotient X of bi-elliptic surface by a finite automorphism group. If X is smooth, then it is a bi-elliptic surface or ruled surface with irregularity one. As a corollary any bi-elliptic surface cannot be Galois covering of…

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…

By a $B$-regular variety, we mean a smooth projective variety over $C$ admitting an algebraic action of the upper triangular Borel subgroup $B \subset SL_2(C)$ such that the unipotent radical in $B$ has a unique fixed point. A result of M.…

For an orbifold X which is the quotient of a manifold Y by a finite group G we construct a noncommutative ring with an action of G such that the orbifold cohomology of X as defined in math.AG/0004129 by Chen and Ruan is the G invariant…