Related papers: Connected components of Prym eigenform loci in gen…

We generalise a result from [Bak15] on K3 type hyperk\"ahler manifolds proving that a line in a lagrangian plane on a hyperk\"ahler manifold $X$ of Kummer type has Beauville-Bogomolov-Fujiki square $-\frac{n+1}{2}$ and order 2 in the…

This paper extends joint work with R. Friedman to show that the closure of the locus of intermediate Jacobians of smooth cubic threefolds, in the moduli space of principally polarized abelian varieties (ppav's) of dimension five, is an…

The geometry of Sp(3)/U(3) as a subvariety of Gr(3,6) is explored to explain several examples given by Mukai of non-abelian Brill-Noether loci, and to give some new examples. These examples identify Brill-Noether loci of vector bundles on…

Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The Prym variety associated to a double cover is a quadratic twist of the Jacobian of a genus three curve X. The curve X…

We construct a "Hitchin-type" connection on bundles of non-abelian theta functions on higher-rank Prym varieties, for unramified double covers of curves. We formulate a version of level-rank duality in this Prym setting (building on work of…

For $g \ge 5$, we give a complete classification of the connected components of strata of abelian differentials over Teichm\"uller space, establishing an analogue of Kontsevich and Zorich's classification of their components over moduli…

In two fundamental classical papers, Masur and Veech have independently proved that the Teichmueller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore…

We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the…

Let k be an algebraically closed field and let HaG(d) be the open locus inside H(d) (the Hilbert scheme of 0-dimensional length d subschemes of the projective (d-2)-space over k) corresponding to arithmetically Gorenstein subschemes. We…

We study fixed loci of antisymplectic involutions on projective hyperk\"ahler manifolds of $\mathrm{K3}^{[n]}$-type. When the involution is induced by an ample class of square 2 in the Beauville-Bogomolov-Fujiki lattice, we show that the…

Let $X$ be a compact connected Riemann surface of genus at least two. Let $M_H(r,d)$ denote the moduli space of semistable Higgs bundles on $X$ of rank $r$ and degree $d$. We prove that the compact complex Bohr-Sommerfeld Lagrangians of…

We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $\nu$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that…

The moduli stack of Deligne-Mumford stable curves of genus g admits a stratification, so that the number of nodes of the curves belonging to one stratum is constant. The irreducible components of the stratum corresponding to curves with…

Let $\phi:\,X\rightarrow Y$ be a (possibly ramified) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of $\phi$, up to isogeny, as the Jacobian of a quotient curve $C$ in the Galois…

In this paper we construct Shimura subvarieties of dimension bigger than one of the moduli space of polarised abelian varieties of a given dimension, which are generically contained in the Pym loci of (ramified) double covers. The idea is…

Let M be a compact closed non-orientable surface. We show that the space of representations of the fundamental group of M into PSL(2,R) has exactly two connected components. These two components are the preimages of a certain…

We show that every GL(2, R) orbit closure of translation surfaces is either a connected component of a stratum, the hyperelliptic locus, or consists entirely of surfaces whose Jacobians have extra endomorphisms. We use this result to give…

Let $G$ be a simple, simply-connected complex algebraic group with Lie algebra $\mathfrak{g}$, and $G/B$ the associated complete flag variety. The Hochschild cohomology $HH^\bullet(G/B)$ is a geometric invariant of the flag variety related…

The local invariants of a meromorphic Abelian differential on a Riemann surface of genus $g$ are the orders of zeros and poles, and the residues at the poles. The main result of this paper is that with few exceptions, every pattern of…

Let $(X,L,V)$ be a triplet where $X$ is an irreducible smooth complex projective variety, $L$ is an ample and spanned line bundle on $X$ and $V\subseteq H^0(X,L)$ spans $L$. The discriminant locus $\Cal D(X,V) \subset |V|$ is the algebraic…