Related papers: Small Instantons, del Pezzo Surfaces and Type I' t…
With the perspective of looking for experimentally detectable physical applications of the so-called topological embedding, a procedure recently proposed by the author for quantizing a field theory around a non-discrete space of classical…
The moduli space of spiked instantons that arises in the context of the BPS/CFT correspondence is realised as the moduli space of classical vacua, i.e. low-energy open string field configurations, of a certain stack of intersecting…
This is an expanded version of our work [AN88], 1988, in Russian. We classify del Pezzo surfaces over C with log terminal singularities of index \le 2. By classification, we understand a description of the intersection graph of all…
We point out that the singular instanton of Hawking-Turok type, in which the singularity occurs due to the divergence of a massless scalar field, can be generated by Euclideanized regular $p$-brane solutions in string (or M-) theory upon…
We show how to construct the general action coupling (multi)instantons to gauge theories arising from branes probing arbitrary toric singularities. We give a general set of rules for how to construct such an action given the knowledge of…
We classify the automorphism groups of del Pezzo surfaces of degrees one and two over an algebraically closed field of characteristic two. This finishes the classification of automorphism groups of del Pezzo surfaces in all characteristics.
We survey the authors recent works, joint with A. Jacob, on Strominger-Yau-Zaslow mirror symmetry for rational elliptic surfaces and del Pezzo surfaces. We discuss some applications, including the Torelli theorem for $ALH^*$ gravitational…
We investigate exceptional sheaves on the Hirzebruch surface $\mathbb{F}_2$, as the first attempt toward the classification of exceptional objects on weak del Pezzo surfaces.
We suggest that superbursts from some low mass X-ray binaries may be due to breaking and re-formation of diquark pairs, on the surface of realistic strange stars. Diquarks are expected to break up due to the explosion and shock of the…
We consider the gauge neutral matter in the low--energy effective action for string theory compactification on a \cym\ with $(2,2)$ world--sheet supersymmetry. At the classical level these states (the \sing's of $E_6$) correspond to the…
We completely classify redundant blow-ups appearing in the theory of rational surfaces with big anticanonical divisor due to Sakai. In particular, we construct a rational surface with big anticanonical divisor which is not a minimal…
We study models of emergent space associated with the Coulomb branch, non-commutative and beta deformations of the N=4 super Yang-Mills theory, extending a previous work on the undeformed conformal case. The idea is to compute the effective…
D-instanton calculus has proved to be able to probe the AdS near horizon geometry for $N$ D-branes systems which, when decoupled from gravity, yield four dimensional superconformal gauge theories with various matter content. In this work we…
We pursue the intriguing possibility that larger-size instantons build up diffractive scattering, with the marked instanton-size scale $<\rho> \approx 0.5$ fm being reflected in the conspicuous ``geometrization'' of soft QCD. As an explicit…
We investigate membrane and fivebrane instanton effects in type IIA string theory compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet, in four dimensional…
We demonstrate the existence of sudden, finite-time, singularities, with constant scale factor, expansion rate and density, in expanding Bianchi type IX universes with free anisotropic pressures. A new type of non-simultaneous anisotropic…
This paper surveys recent progress towards the Manin conjecture for (singular and non-singular) del Pezzo surfaces. To illustrate some of the techniques available, an upper bound of the expected order of magnitude is established for a…
In both Yang-Mills theories and sigma models, instantons are endowed with degrees of freedom associated to their scale size and orientation. It has long been conjectured that these degrees of freedom have a dual interpretation as the…
In this paper we study quotients of del Pezzo surfaces of degree four and more over arbitrary field $\Bbbk$ of characteristic zero by finite groups of automorphisms. We show that if a del Pezzo surface $X$ contains a point defined over the…
We study intersections of exceptional curves on del Pezzo surfaces of degree 1, motivated by questions in arithmetic geometry. Outside characteristics 2 and 3, at most 10 exceptional curves can intersect in a point. We classify the…