Stable pairs on nodal K3 fibrations

We study Pandharipande-Thomas's stable pair theory on $K3$ fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of Kawai-Yoshioka's formula for the Euler characteristics of moduli spaces of stable pairs on $K3$ surfaces and Noether-Lefschetz numbers of the fibration. Moreover, we investigate the relation of these invariants with the perverse (non-commutative) stable pair invariants of the $K3$ fibration. In the case that the $K3$ fibration is a projective Calabi-Yau threefold, by means of wall-crossing techniques, we write the stable pair invariants in terms of the generalized Donaldson-Thomas invariants of 2-dimensional Gieseker semistable sheaves supported on the fibers.Comment: Published versio

On topological approach to local theory of surfaces in Calabi-Yau threefolds

We study the web of dualities relating various enumerative invariants, notably Gromov-Witten invariants and invariants that arise in topological gauge theory. In particular, we study Donaldson-Thomas gauge theory and its reductions to D=4 and D=2 which are relevant to the local theory of surfaces in Calabi-Yau threefolds.Comment: 38 pages, To Appear in Adv. Theor. Math. Phys. (2017

Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds

An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold

A novel proton transfer self-associated compound from dipicolinic acid and guanidine and its Cadmium(II) complex: synthesis, characterization, crystal structure, and solution studies

A novel 1:2 proton transfer self-associated compound LH2, (GH+)2(pydc2—), was synthesized from the reaction of dipicolinic acid, pydcH2, (2, 6-pyridinedicarboxylic acid), and guanidine hydrochloride, (GH+)(Cl—). The characterization was performed using IR, 1H and 13C NMR spectroscopy and single-crystal X-ray diffraction. LH2 · H2O crystallizes in the space group C2/c of the monoclinic system and contains eight molecules per unit cell. The unit cell dimensions are: a = 26.480(5)Å, b = 8.055(2)Å, c = 14.068(3)Å. The first coordination complex (GH)2[Cd(pydc)2] · 2H2O, was prepared using LH2 and cadmium(II) iodide, and characterized by 1H and 13C NMR spectroscopy and X-ray crystallography. The crystal system is triclinic with space group P1¯ with one molecule per unit cell. The unit cell dimensions are: a = 8.5125(7)Å, b = 11.0731(8)Å, c = 13.2404(10)Å. The cadmium(II) atom is six-coordinated with a distorted octahedral geometry. The two pydc2— units are almost perpendicular to each other. The protonation constants of the building blocks of the pydc-guanidine adduct, the equilibrium constants for the reaction of pydc2— with guanidine and the stoichiometry and stability of the Cd2+ complex with LH2 in aqueous solution were accomplished by potentiometric pH titration. The solution studies strongly support a self-association between pydc2— and GH+ with a stoichiometry for the CdII complex similar to that observed for the isolated crystalline complex. In fact, the [Cd(pydc)2]2— complex was found as the most abundant species in solution (> 90 %) at a pH >5

Characterization, crystal structure, and solution studies of a proton transfer compound obtained from 2,6-pyridinedicarboxylic acid and 1,4,10,13-tetraoxa-7,6-diazacyclooctadecane

The pro ton trans fer com pound, (DA18C6H2)(pydcH)2×0.25H2O, has been pre pared from the re ac tion be tween 1,4,10,13-tetraoxa-7,16-diazacyclooctadecane, diaza-18-crown-6 (DA18C6), and 2,6-pyridinedicarboxylic acid, dipicolinic acid (pydcH2). The char ac ter iza tion was per formed us ing 1H and 13C NMR, IR spec tros copy and sin gle crys tal X-ray dif frac tion anal y sis. The asym met ric unit con sists of one (DA18C6H2)2+ cat ion adopt ing a sigmoidal con for ma tion which in ter acts with two (pydcH)– an ions via hy dro gen bonds in volv ing the protonated amine groups of the diazacrown ether. –COOH···–OOC– head-to-tail hy dro gen bonds gen er ate 2D un du lat - ing lay ers along [100] and [001] in the crys tal lat tice. The protonation con stants of DA18C6 and pydcH2 and equi lib rium con stants for the re ac tion of the two re ac tants were de ter mined by potentiometric pH ti tra tion. The so lu tion stud ies sup ported the for ma tion also in so lu tion of (DA18C6H2)(pydcH)2 as the most abun dant spe cies at pH = 3.4