Related papers: Minimal Model Program with scaling and adjunction …

We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…

Let $X$ be a projective variety over a field. In this paper, we will construct a moduli space of very ample line bundles on $X$. In doing so, we develop a generalization of Fitting ideals to complexes of sheaves on $X$. We give other…

We introduce a notion of Homological Projective Duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties $X$ and $Y$ in dual projective spaces are…

Let $G$ be an algebraic group and let $X$ be a smooth $G$-variety with two orbits: an open orbit and a a closed orbit of codimension $1$. We give an algebraic description of the category of $G$-equivariant vector bundles on $X$ under a mild…

Let $(X, \Delta)$ be a projective klt three dimensional pair defined over an algebraically closed field characteristic larger than 5. Let $L$ be a nef and big line bundle on $X$ such that $L-K_X-\Delta$ is big and nef. We show that $L$ is…

We develop a bundle theory of presheaves on small categories, based on similar work by Brent Everitt and Paul Turner. For a certain set of presheaves on posets, we produce a Leray-Serre type spectral sequence that gives a reduction property…

The notes start with an elementary introduction to a few important analytic techniques of algebraic geometry: closed positive currents, $L^2$ estimates for the $\dbar$-operator on positive vector bundles, Nadel's vanishing theorem for…

This paper proposes a new generalized linear model with the fractional binomial distribution. Zero-inflated Poisson/negative binomial distributions are used for count data with many zeros. To analyze the association of such a count variable…

In this paper, we investigate properties of potential triples $(X,\Delta,D)$ which consists of a pair $(X,\Delta)$ and a pseudoeffective $\mathbb{R}$-Cartier divisor $D$. In particular, we show that if $D$ admits a birational Zariski…

We show that birational smooth complex projective varieties with numerically effective canonical bundles along the exceptional loci have the same Betti numbers. In particular, birational smooth minimal models share the same Betti numbers.…

Let $X,Y$ be two irreducible subvarieties of the projective space $\mathbb{P}^n$, and $d\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\bf explicitly}, in terms of $d$ and the ideals defining $X$ and…

The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, $Z$, is then linear in the number of categories, which is…

We relate Nakajima Quiver Varieties (or, rather, their multiplicative version) with moduli spaces of perverse sheaves. More precisely, we consider a generalization of the concept of perverse sheaves: microlocal sheaves on a nodal curve X.…

We study a scheme M closely related to the set of pairs of n by n-matrices with rank 1 commutator. We show that M is a reduced complete intersection with n+1 irreducible components, which we describe. There is a distinguished Lagrangian…

Let $X$ be a weakly pseudoconvex manifold and $L\longrightarrow X$ be a holomorphic line bundle with a singular positive Hermitian metric $h$. In this article, we provide a points separation theorem and an embedding for the adjoint linear…

Motivated by renal imaging studies that combine renogram curves with pharmacokinetic and demographic covariates, we propose Hybrid partial least squares (Hybrid PLS) for simultaneous supervised dimension reduction and regression in the…

On a smooth complex projective variety $X$ of dimension $n$, consider an ample vector bundle $\mathcal{E}$ of rank $r \leq n-2$ and an ample line bundle $H$. A numerical character $m_2=m_2(X,\mathcal{E},H)$ of the triplet…

How likely is it that there are particles in a vector-like pair of representations in low-energy spectrum, when neither symmetry nor anomaly consideration motivates their presence? We address this question in the context of supersymmetric…

We prove a part of Shokurov's conjecture on characterization of toric varieties modulo the minimal model program and adjunction conjecture.

Let $X$ be a del Pezzo surface. When the degree of $X$ is at least 4, we compute the cohomology of a general sheaf in the moduli space of Gieseker semistable sheaves. We also classify the Chern characters for which the general sheaf in the…