arXiv research

Characterizes Wahl singularities in del Pezzo surface degenerations.

In this paper we study the problem of existence of orbifold Kaehler-Einstein metrics on del Pezzo surfaces of degree 1 with Du Val singular points. Moreover we compute global log canonical thresholds of del Pezzo surfaces of degree 1 with Du Val singularities and of del Pezzo surfaces of Picard rank 1 with Du Val singu…

We study global log canonical thresholds of del Pezzo surfaces.

A smooth curve found in a space of special surfaces.

We prove functional identities for conic webs on del Pezzo surfaces.

We classify smooth del Pezzo surfaces whose alpha-invariant of Tian is bigger than one.

In this note, we compute the Poisson cohomology groups for any Poisson Del Pezzo surface.

Study finds limits for conical Kähler-Einstein metrics on unstable surfaces.

We apply Nadel's method of multiplier ideal sheaves to show that every complex del Pezzo surface of degree at most six whose automorphism group acts without fixed points has a Kähler-Einstein metric. In particular, all del Pezzo surfaces of degree $4,5$, or $6$ and certain special del Pezzo surfaces of lower degree are…

We prove new local inequality for divisors on surfaces and utilize it to compute $α$-invariants of singular del Pezzo surfaces, which implies that del Pezzo surfaces of degree one whose singular points are of type $\mathbb{A}_{1}$, $\mathbb{A}_{2}$, $\mathbb{A}_{3}$, $\mathbb{A}_{4}$, $\mathbb{A}_{5}$ or $\mathbb{A}_{6…

Real del Pezzo surfaces split real lines into elliptic and hyperbolic types.

We describe a framework for constructing the general Ricci-flat metric on the anticanonical cone over the del Pezzo surface of rank one.

We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$. As a corollary we obtain the existence of orbifold Kähler--Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well-…

We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them.

We study del Pezzo surfaces that are quasismooth and well-formed weighted hypersurfaces. In particular, we find all such surfaces whose alpha-invariant of Tian is greater than 2/3.

The paper proves mirror symmetry for del Pezzo surfaces and computes related structures.

We prove that the Gromov-Hausdorff compactification of the moduli space of Kahler-Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification. In particular, this recovers Tian's theorem on the existence of Kahler-Einstein metrics on smooth Del Pezzo surfaces and classifies the deg…

We give a simple sufficient condition for K-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kahler metric in the Kahler class corresponding to the polarization.

Study identifies Kähler-Einstein, Kähler-Ricci soliton, and Sasaki-Einstein metrics on log del Pezzo surfaces.

The study classifies involutions on del Pezzo surfaces.

Lagrangian spheres in the symplectic Del Pezzo surfaces arising as blow-ups of the complex projective plane in 4 or fewer points are classified up to Lagrangian isotopy. Unlike the case of the 5-point blow-up, there is no Lagrangian knotting.

From a hermitian metric on the anticanonical bundle on a Del Pezzo surface, and a holomorphic section of it, we construct a one parameter family of bihermitian metrics (or equivalently generalized Kaehler structures). The construction appears to be linked to noncommutative geometry.

Study real Mordell-Weil group and real lines on rational elliptic surfaces and del Pezzo surfaces.

The global log canonical threshold (or Tian's alpha-invariant) plays an important role in the geometry of Fano varieties. Tian showed that Fano manifolds with big alpha-invariant can be equipped with a Kahler-Einstein metric. In recent years Donaldson drafted a programme to determine when a smooth Fano variety X admits…

Recent state-of-the-art natural language understanding models, such as BERT and XLNet, score a pair of sentences (A and B) using multiple cross-attention operations - a process in which each word in sentence A attends to all words in sentence B and vice versa. As a result, computing the similarity between a query sente…

A deep probabilistic model analyzes DNA-encoded library data for efficient screening.

Researchers compute monodromy groups of surface families over quartic curves.

Researchers prove mirror symmetry for certain non-compact Calabi-Yau surfaces.

Study real algebraic curves on real del Pezzo surfaces using degeneration methods.

In this paper we prove that generic small partial smoothings of Kahler-Einstein (KE) Del Pezzo orbifolds with only nodal singularities, and with no non-zero holomorphic vector fields, admit orbifold KE metrics which are close in the Gromov-Hausdorff sense to the original KE metric.

Researchers solved a complex problem for a specific type of 4-manifolds.

Estimating the difficulty level of math word problems is an important task for many educational applications. Identification of relevant and irrelevant sentences in math word problems is an important step for calculating the difficulty levels of such problems. This paper addresses a novel application of text categoriza…

Study monodromy factorizations for lines on del Pezzo surfaces.

The second del Pezzo surface is known by work of Tian-Zhu and Wang-Zhu to admit a unique Kaehler-Ricci soliton. Applying a method described in hep-th/0703057, we use Ricci flow to numerically compute that soliton metric. We numerically compute the value of its Perelman entropy (or Gaussian density).

New metrics predict human sentence comprehension across languages.

On certain del Pezzo surfaces with large automorphism groups, it is shown that the solution to the Kähler-Ricci flow with a certain initial value converges in $C^\infty$-norm exponentially fast to a Kähler-Einstein metric. The proof is based on the method of multiplier ideal sheaves.

Let $(X, J)$ be a compact Kahler manifold with a non-zero holomorphic Poisson structure $β$. If the obstruction space for deformations of generalized complex structures on $(X, J)$ vanishes, we obtain a family of deformations of non-trivial bihermitian structures $(J, J^-_t, h_t)$ on $X$ by using $β$. In addition, if t…

Given vector representations for individual words, it is necessary to compute vector representations of sentences for many applications in a compositional manner, often using artificial neural networks. Relatively little work has explored the internal structure and properties of such sentence vectors. In this paper, we…

Existing models based on artificial neural networks (ANNs) for sentence classification often do not incorporate the context in which sentences appear, and classify sentences individually. However, traditional sentence classification approaches have been shown to greatly benefit from jointly classifying subsequent sente…

We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces X and vector fields v which are K-stable in the sense of Berman-Nystrom and therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide some new examples of Fano threefolds admitting a Kahler-Ricci soliton.

We propose a new generative model of sentences that first samples a prototype sentence from the training corpus and then edits it into a new sentence. Compared to traditional models that generate from scratch either left-to-right or by first sampling a latent sentence vector, our prototype-then-edit model improves perp…

Paper proposes a novel model to improve n-ary cross-sentence relation extraction by addressing noisy data and non-consecutive sentences.

The paper proves K-stability of special Gushel-Mukai manifolds.

Proves SYZ mirror symmetry for del Pezzo and rational elliptic surfaces.

The aim of this paper is to construct infinitely many families of Einstein metrics on the connected sums of arbitrary number of copies of $S^2\times S^3$. We realize these 5-manifolds as total spaces of Seifert bundles over Del Pezzo orbifolds. A Kähler--Einstein metric on the Del Pezzo orbifold is then lifted to an Ei…

Distributed representations of sentences have become ubiquitous in natural language processing tasks. In this paper, we consider a continual learning scenario for sentence representations: Given a sequence of corpora, we aim to optimize the sentence encoder with respect to the new corpus while maintaining its accuracy …

In real-world applications of natural language generation, there are often constraints on the target sentences in addition to fluency and naturalness requirements. Existing language generation techniques are usually based on recurrent neural networks (RNNs). However, it is non-trivial to impose constraints on RNNs whil…

Unsupervised scheme ranks sentences in text documents based on semantic importance.