Related papers: Some remarks on Gopakumar-Vafa invariants

We introduce a diffeomorphism invariant of $4$-manifolds, the $\mathrm{Pin}^-(2)$-monopole invariant, defined by using the $\mathrm{Pin}^-(2)$-monopole equations. We compute the invariants of several $4$-manifolds, and prove gluing…

Let A be a commutative Noetherian local ring containing a field of characteristic p>0. The integer invariants $\lambda_{i,j}(A)$ have been introduced in an old paper of ours. In this paper we completely describe $\lambda_{d,d}(A)$, where…

We study the problem of computing Gopakumar-Vafa invariants for multiparameter families of symmetric Calabi-Yau threefolds admitting flops to diffeomorphic manifolds. There are infinite Coxeter groups, generated by permutations and flops,…

We consider the moduli space of rank two, odd degree, semi-stable Real vector bundles over a real curve, calculating the singular cohomology ring in odd and zero characteristic for most examples.

In this short note we provide a proof that the Chern-Simons part of the action for N D-branes is invariant under gauge transformations of the RR fields of the type C_p ->C_p + d\Lambda_{p-1}, and rewrite the action in a form that makes this…

A mechanism to find different Weyl invariant p-branes and Dp-branes actions is explained. Our procedure clarifies the Weyl invariance for such systems. Besides, by considering gravity-dilaton effective action in higher dimensions we also…

We introduce a new action $S_{standard}^{(\rho,h; \Phi,g,B,C)}$ for D-branes that is to D-branes as the Polyakov action is to fundamental strings. This `standard action' is abstractly a non-Abelian gauged sigma model --- based on maps…

The phase transitions are studied for the D-brane systems with multiple open-string moduli in terms of toric geometry: between the parallel D-brane phase corresponding to the Coulomb branch and the coincident phase corresponding to the…

We briefly review a covariant analysis of D-branes of type IIB superstring on the AdS_5xS^5 background from the \kappa-invariance of the Green-Schwarz string action. The possible configurations of D-branes preserving half of supersymmetries…

We study from an algebraic point of view the question of extending an action of a group \(\Gamma\) on a commutative domain \(R\) to a formal pseudodifferential operator ring \(B=R(\!(x\,;\,d)\!)\) with coefficients in \(R\), as well as to…

Two examples of $\mathrm{Diff}^+S^1$-invariant closed two-forms obtained from forms on jet bundles, which does not admit equivariant moment maps are presented. The corresponding cohomological obstruction is computed and shown to coincide…

We compute the integer cohomology rings of the ``polygon spaces'' introduced in [Hausmann,Klyachko,Kapovich-Millson]. This is done by embedding them in certain toric varieties; the restriction map on cohomology is surjective and we…

We represent in this preprint the exact estimate for covariation berween two random variables (r.v.), which are measurable relative the corresponding sigma-algebras through anyhow mixing coefficients. We associate a solution of this problem…

We study gauge theories based on nonabelian 2-forms. Certain connections on loop space give rise to generalized covariant derivatives that include a nonabelian 2-form. This can be used to find rather straightforward expressions for the…

We consider a $\sigma$-model formulation of open string theory in the presence of D-branes. We perform two-loop computations and discuss gravitational corrections to Born-Infeld action when branes are non-trivially embedded in a curved…

We compute the rational cohomology ring of \bar R_2, the (compactified) moduli space of Prym curves of genus 2. We also recompute the rational cohomology ring of \bar S_2, the moduli space of spin curves of genus 2, thereby correcting some…

Let Vect(R) be the Lie algebra of smooth vector fields on R. The space of symbols Pol(T^* R) admits a non-trivial deformation (given by differential operators on weighted densities) as a Vect(R)-module that becomes trivial once the action…

We show that the moduli stacks of semistable sheaves on smooth projective varieties are analytic locally on their coarse moduli spaces described in terms of representations of the associated Ext-quivers with convergent relations. When the…

A moduli space of stable maps to the fibers of a fiber bundle is constructed. The new moduli space is a family version of the classical moduli space of stable maps to a non-singular complex projective variety. The virtual cycle for this…

This article constructs Von Neumann invariants for constructible complexes and coherent D-modules on compact complex manifolds, generalizing the work of the author on coherent L 2-cohomology. We formulate a conjectural generalization of…