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This paper concerns Waring decompositions of a certain kind of plane quartics of high rank. The main result is the following. Let x, l_1, ...., l_7 be linear forms and q a quadratic form on a K-vector...
A symplectic or orthogonal bundle $V$ of rank $2n$ over a curve has an invariant $t(V)$ which measures the maximal degree of its isotropic subbundles of rank $n$. This invariant $t$ defines stratifica...
In geometric terms, given a singular foliation of the plane, a dicritical divisor is (whenever it exists) an irreducible component of the exceptional divisor which is transverse to the foliation. Abhy...
We give a cohomological classification of vector bundles on smooth affine threefolds over algebraically closed fields having characteristic unequal to 2. As a consequence, if A is a smooth affine alge...
We show that any extremal contraction from a smooth projective variety with dimension less than or equal to three appears as a moduli space of (semi)stable objects in the derived category of coherent ...
This note is a gentle introduction to higher dimensional local fields, with the motivating problem being the standard geometric "localisation-completion" process by which they can be constructed. A di...
In this paper we construct a tilting sheaf for Severi-Brauer Varieties and Involution Varieties. This sheaf relates the derived category of each variety to the derived category of modules over a ring ...
We describe noncommutative desingularizations of determinantal varieties, determinantal varieties defined by minors of generic symmetric matrices, and pfaffian varieties defined by pfaffians of generi...
Let $F$ be a homogeneous polynomial in $S = \mathbb{C}[x_0,...,x_n]$. Our goal is to understand a particular polynomial decomposition of $F$; geometrically, we wish to determine when the hypersurface ...
We obtain a formula for the generating series of (the push-forward under the Hilbert-Chow morphism of) the Hirzebruch homology characteristic classes of the Hilbert schemes of points for a smooth quas...
We apply the results of arXiv:1109.3573 to study quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps...
We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of totally isotropic subspa...
A general strategy is given for the classification of graphs of rational surface singularities. For each maximal rational double point configuration we investigate the possible multiplicities in the f...
The purpose of this paper is to establish an effective non-vanishing theorem for the syzygies of an adjoint-type line bundle on a smooth variety, as the positivity of the embedding increases. Our purp...
The constancy of the Milnor number has several characterizations which were summarized by Greuel in 1986. This paper presents a study of these characterizations in the case of families of functions wi...

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