Related papers: Hartogs and open embeddings, proper maps, compacti…

Definable subcategories may be extended along a ring homomorphism directly, by using their defining conditions in the new module category, or by tensoring up with the new ring. We investigate what is preserved and reflected by these…

This paper provides a systematic treatment of Gorenstein homological aspects for cleft extensions of rings. In particular, we investigate Goresnteinness, Gorenstein projective modules and singularity categories in the context of cleft…

Given a bounded complex of finitely generated modules $M$ over a commutative noetherian local ring $R$, one assigns to it a variety, $\mathcal V_R(M)$, called the cohomological support variety of $M$ over $R$. The variety $\mathcal V_R(M)$…

We introduce the homogeneous and piecewise multilinear extensions and the eigenvalue problem for locally Lipschitz function pairs, in order to develop a systematic framework for relating discrete and continuous min-max problems. This also…

This is an expository article on the recent developments of Hodge theory on moduli spaces of smooth projective varieties with semi-ample canonical line bundles.

We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular…

The main purpose of this paper is to generalize the celebrated L${}^2$ extension theorem of Ohsawa-Takegoshi in several directions : the holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety…

Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the…

This thesis contributes with a number of topics to the subject of string compactifications. In the first half of the work, I discuss the Hodge plot of Calabi-Yau threefolds realised as hypersurfaces in toric varieties. The intricate…

We show that geometric syntomic cohomology lifts canonically to the category of Banach-Colmez spaces and study its relation to extensions of modifications of vector bundles on the Fargues-Fontaine curve. We include some computations of…

In this paper we study cobordism categories consisting of manifolds which are endowed with geometric structure. Examples of such geometric structures include symplectic structures, flat connections on principal bundles, and complex…

In this article, for singular hermitian metrics on holomorphic vector bundles, we consider minimal $L^2$ integrals on sublevel sets of plurisubharmonic functions on weakly pseudoconvex K\"ahler manifolds related to modules at boundary…

In this paper we consider the complex vector spaces of holomorphic cross-sections of homogeneous holomorphic vector bundles over elliptic adjoint orbits, and provide a sufficient condition for the vector spaces to be finite dimensional in…

We discuss some finite homogeneous structures, addressing the question of universality of their automorphism groups. We also study the existence of so-called Kat\v{e}tov functors in finite categories of embeddings or homomorphisms.

Let $X$ be a Hilbert modular variety and $\mathbb{V}$ a non-trivial local system over $X$ with infinite monodromy. In this paper we study Saito's mixed Hodge structure (MHS) on the cohomology group $H^k(X,\mathbb{V})$ using the method of…

We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic…

The relationship between associative composition algebras of dimensions 2 and 4 within the context of homogeneous spaces, with a particular focus on Hamiltonian quaternions, is explored. In the special case of Hamiltonian quaternions, the…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

Let $X$ be the special fiber of a unitary Shimura variety of hyperspecial level at a prime $p$ inert in the totally real field $F$. Let $Y\to X$ be the associated flag space. For every $L$-dominant weight $\lambda$, let…

Working in the category of smooth projective varieties over an algebraically closed field of characteristic 0, we review notions of ampleness and numerical nefness for Higgs bundles which "feel" the Higgs field and formulate criteria of the…