Related papers: Functorial destackification and weak factorization…
In this paper we study skeleta of residually tame coverings of a marked curve over a non-archimedean field. We first generalize a result by Liu and Lorenzini by proving a simultaneous semistable reduction theorem for residually tame…
We generalize theorems of Deligne-Mumford and de Jong on semi-stable modifications of families of proper curves. The main result states that after a generically \'etale alteration of the base any (not necessarily proper) family of…
Families of stable curves of genus $\gamma$ over a smooth curve $C$ correspond to morphisms from $C$ to the moduli stack of stable curves $\bar{\cal M}_\gamma$. It is natural to compactify the corresponding moduli problem using stable maps…
For a cyclic group $G$ acting on a smooth variety $X$ with only one character occurring in the $G$-equivariant decomposition of the normal bundle of the fixed point locus, we study the derived categories of the orbifold $[X/G]$ and the…
Let G be a split reductive group. We introduce the moduli problem of "bundle chains" parametrizing framed principal G-bundles on chains of lines. Any fan supported in a Weyl chamber determines a stability condition on bundle chains. Its…
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 if $X$ is a smooth quasi-projective $3$-fold admitting a flopping contraction, then the fundamental group of an associated simplicial hyperplane arrangement acts faithfully on the derived category of $X$. The main technical…
We give a classification of smooth complex manifolds with a finite abelian group action, such that the quotient is isomorphic to a projective space. The case where the manifold is a Calabi-Yau is studied in detail.
We study holomorphic foliations of aribitrary codimension in smooth complete toric varieties. We show that split foliations are stable if some good behaviour of their singular set is provided. As an application of these results, we exhibit…
Let X be an abelian scheme over a scheme B. The Fourier--Mukai transform gives an equivalence between the derived category of X and the derived category of the dual abelian scheme. We partially extend this to certain schemes X over B (which…
We describe the effect of ramified morphisms on Harbourne constants of reduced effective divisors. With this goal, we introduce the pullback of a weighted cluster of infinitely near points under a dominant morphism between surfaces, and…
In this article we prove a sharp decay estimate for certain multilinear oscillatory integral operators of a form inspired by the general framework of Christ, Li, Tao, and Thiele [6]. A key purpose of this work is to determine when such…
The elementary resolution of singularities algorithm of the author's earlier paper (math.CA/0609217) is developed further, replacing the quasibump functions in the blown up coordinates with the characteristic function of a rectangle times a…
In this thesis we present an introduction to Soft-Collinear Effective Theory, which can be used to prove (or disprove) factorization theorems to all orders in the strong coupling constant for some B decays into light and energetic…
This article is based on a talk given at the Kinosaki Symposium on Algebraic Geometry in 2015, about a work in progress. We describe a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. We explicitly…
We consider degenerations of all simple Lie algebras of exceptional type obtained by embedding into affine Lie algebras. We give a filtration to consider this as an abelianisation of the original Lie algebra. We then show that the…
We introduce a new geometric approach to a manifold equipped with a smooth density function that takes a torsion-free affine connection, as opposed to a weighted measure or Laplacian, as the fundamental object of study. The connection…
We present a definition of stable family of foliations and show that the corresponding moduli functor for foliated surfaces is representable by a Deligne-Mumford stack.
Results due to Druel and Beauville show that the blowup of the intermediate Jacobian of a smooth cubic threefold X in the Fano surface of lines can be identified with a moduli space of semistable sheaves of Chern classes c_1=0, c_2=2, c_3=0…
We introduce a notion of Gieseker stability for coherent sheaves on tame Deligne-Mumford stacks with projective moduli scheme and some chosen generating sheaf on the stack in the sense of Olsson and Starr \cite{MR2007396}. We prove that…