THE FATTY AND FIBROID DEGENERATIONS.

Corneal Degenerations

Degenerations are defi ned as the gradual deterioration of a tissue or an organ that was previously normal with frequent loss of functional activity. Corneal degenerations are characterized by the deposition of material, thinning of tissue, and vascularization. Contrary to corneal dystrophies, they are not hereditary and could be unilateral. Moreover, because of the continuous exposure to envir...

The Ruled Vertex and D - E Degenerations

We compute all genus topological amplitudes on configurations of ruled surfaces obtained by resolving lines of D-E singularities in compact Calabi-Yau threefolds. We find that our results are in agreement with genus zero mirror symmetry calculations, which is further evidence for the validity of the ruled vertex formalism for degenerate torus actions. ∗[email protected] †florea@physics...

Fibroid Polypus

Degenerations of the Veronese and Applications

The classical Hermite interpolation technique approximates a given differentiable function defined in an open subset of R with a polynomial of a given degree which takes at an assigned set points p1, . . . , pn, usually assumed to be sufficiently general, the same values as the function and of its derivatives up to orderm1, . . . ,mn respectively. A geometric counterpart of Hermite interpolatio...

Degenerations of Abelian Differentials

Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate differentials, give dimension bounds for their moduli spaces, and establish smoothability criteria. As applications, we show that the spin parity of holomorphic...