Related papers: Direct images, fields of Hilbert spaces, and geome…

In this paper we study $G$-Higgs bundles over an elliptic curve when the structure group $G$ is a classical complex reductive Lie group. Modifying the notion of family, we define a new moduli problem for the classification of semistable…

We quantize an inhomogeneous cosmological model using techniques that include polymeric quantization. More explicitly, we construct well defined operators to represent the constraints and find the physical Hilbert space formed by their…

In this paper, we explore the quantization of K\"ahler manifolds, focusing on the relationship between deformation quantization and geometric quantization. We provide a classification of degree 1 formal quantizable functions in the…

We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the K\"ahler case, state spaces arise as spaces of…

For a projective morphism of an smooth algebraic surface $X$ onto a smooth algebraic curve $S$, both given over a perfect field $k$, we construct the direct image morphism in two cases: from $H^i(X,\Omega^2_X)$ to $H^{i-1}(S,\Omega^1_S)$…

Given a compact K\"ahler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic vector bundles containing the coarse moduli space of…

We generalise the notions of scalar-valued holomorphic $p$-contact and $s$-symplectic structures introduced recently on compact complex manifolds by the second-named author jointly with H. Kasuya and L. Ugarte to their analogues with values…

In this short paper we combine the representability theorem introduced in [17, 18] with the theory of derived formal models introduced in [2] to prove the existence representability of the derived Hilbert space RHilb(X) for a separated…

Riemann--Hilbert techniques are used in the theory of completely integrable differential equations to generate solutions that contain a free function which can be used at least in principle to solve initial or boundary value problems. The…

This is an expository article. In the first part we recall the definition and a few results concerning singular Hermitian metrics on torsion-free coherent sheaves. They offer the perfect platform for the study of properties of direct images…

We detect Hilbert manifolds among isometrically homogeneous metric spaces and apply the obtained results to recognizing Hilbert manifolds among homogeneous spaces of the form G/H where G is a metrizable topological group and H is a closed…

A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on…

Let $\pi : \mathcal X \to S$ be a local universal family of compact Ricci-flat K\"ahler manifolds over a smooth base $S$. The complexified K\"ahler cones of each fiber of the family form a holomorphic fiber bundle $\mathcal K \to S$. We…

We show that a singular Hermitian metric on a holomorphic vector bundle over a Stein manifold which is negative in the sense of Griffiths (resp. Nakano) can be approximated by a sequence of smooth Hermitian metrics with the same curvature…

We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…

Let $f : X \rightarrow Y$ be a separable finite surjective map between irreducible normal projective varieties defined over an algebraically closed field, such that the corresponding homomorphism between \'etale fundamental groups $f_* :…

Progress on the problem whether the Hilbert schemes of locally Cohen-Macaulay curves in projective 3 space are connected has been hampered by the lack of an answer to a question that was raised by Robin Hartshorne in his paper "On the…

Let $K\backslash G$ be an irreducible Hermitian symmetric space of noncompact type and $\Gamma \,\subset\, G$ a closed torsionfree discrete subgroup. Let $X$ be a compact K\"ahler manifold and $\rho\, :\, \pi_1(X, x_0)\,\longrightarrow\,…

In this paper, we investigate the geometry of the base complex manifold of an effectively parametrized holomorphic family of stable Higgs bundles over a fixed compact K\"{a}hler manifold. The starting point of our study is…

It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the…