Related papers: Logarithmic vector fields and the Severi strata in…

We consider, under suitable assumptions, the following situation: $\mathcal B$ is a component of the moduli space of polarized surfaces and $\mathcal V_{m,\delta}$ is the universal Severi variety over $\mathcal B$ parametrizing pairs…

Let $\mathcal S\to\mathbb A^1$ be a smooth family of surfaces whose general fibre is a smooth surface of $\mathbb P^3$ and whose special fibre has two smooth components, intersecting transversally along a smooth curve $R$. We consider the…

Let $R$ be a discrete valuation ring, with valuation $v \colon R \twoheadrightarrow \mathbb{Z}_{\ge 0} \cup \{\infty\}$ and residue field $k$. Let $H$ be a hypersurface $\operatorname{Proj}(R[x_0,\ldots,x_n]/\langle f \rangle)$. Let $H_k$…

Let V be a finite dimensional complex vector space and V^* its dual and let X in P(V) be a smooth projective variety of dimension n and degree d at least two. For a generic n-tuple of hyperplanes H_1,...,H_n in P(V^*)^n, the intersection of…

For a linear system $|C|$ on a smooth projective surface $S$, whose general element is a smooth, irreducible curve, the Severi variety $V_{|C|, \delta}$ is the locally closed subscheme of $|C|$ which parametrizes irreducible curves with…

We introduce a phase space with spinorial momenta, corresponding to fermionic derivatives, for a 2d supersymmetric (1, 1) sigma model. We show that there is a generalisation of the covariant De Donder-Weyl Hamiltonian formulation on this…

We study germs of holomorphic distributions with "separated variables'. In codimension one, a well know example of this kind of distribution is given by the canonical contact structure on $\mathbb{P}^{2m+1}$ . Another example is the Darboux…

We attach two binary codes to a projective nodal surface (the strict code K and, for even degree d, the extended code K' ) to investigate the `Nodal Severi varieties F(d, n) of nodal surfaces in P^3 of degree d and with n nodes, and their…

Let $l$ and $p$ be distinct primes, let $F$ be a local field with residue field of characteristic $p$, and let $\mathfrak{X}$ be the irreducible component of the moduli space of Langlands parameters for $GL_3$ over $\mathbb{Z}_l$…

The main goal of this work is to construct and study a reasonable compactification of the strata of the moduli space of Abelian differentials. This allows us to compute the Kodaira dimension of some strata of the moduli space of Abelian…

Smooth complex polarized varieties $(X,L)$ with a vector subspace $V \subseteq H^0(X,L)$ spanning $L$ are classified under the assumption that the locus ${\Cal D}(X,V)$ of singular elements of $|V|$ has codimension equal to $\dim(X)-i$,…

We describe a method for computing discriminants for a large class of families of isolated determinantal singularities -- more precisely, for subfamilies of ${\mathcal G}$-versal families. The approach intrinsically provides a decomposition…

We study the local invariants that a meromorphic $k$-differential on a Riemann surface of genus $g\geq0$ can have. These local invariants are the orders of zeros and poles, and the $k$-residues at the poles. We show that for a given pattern…

If a pure simplicial complex is partitionable, then its $h$-vector has a combinatorial interpretation in terms of any partitioning of the complex. Given a non-partitionable complex $\Delta$, we construct a complex $\Gamma \supseteq \Delta$…

Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplectic and preserves the fibration. We then show an application…

There are two main problems in finding the higher genus superstring measure. The first one is that for $g\geq 5$ the super moduli space is not projected. Furthermore, the supermeasure is regular for $g\leq 11$, a bound related to the source…

Consider a surface $\Omega$ with a boundary obtained by gluing together a finite number of equilateral triangles, or squares, along their boundaries, equipped with a flat unitary vector bundle. Let $\Omega^{\delta}$ be the discretization of…

Let $G$ be a $\mathbb{Q}_p$-split reductive group with connected centre and Borel subgroup $B=TN$. We construct a right exact functor $D^\vee_\Delta$ from the category of smooth modulo $p^n$ representations of $B$ to the category of…

We enumerate the ends of each stratum of meromorphic 1-forms on Riemann surfaces with prescribed multiplicities of zeroes and poles. Our proof uses degeneration techniques based on the construction by…

Fix a field $k$. When $\Delta$ is a simplicial complex on $n$ vertices with Stanley-Reisner ideal $I_\Delta$, we define and study an invariant called the $\textit{type defect}$ of $\Delta$. Except when $\Delta$ is of a single simplex, the…