Let $${\mathcal {K}}$$ denote a nonsingular conic in the projective plane. Pascal’s theorem says that, given six distinct points A, B, C, D, E, F on , three intersection $$AE \cap BF, AD CF, BD CE$$ are collinear. The line containing them is called Pascal of sextuple. However, this construction may fail when some come together. In paper, we find indeterminacy locus where not well-defined and th...

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...

Twenty patients with pigmentary retinal degenerations of various types, nine patients with other ocular and systemic illnesses, and five normal volunteer subjects were tested for cellmediated immunity by the I-iododeoxyuridine (IUDR) cytotoxicity assay, against a longterm tissue culture line derived from retinoblastoma, which by electron microscopy showed evidence of being derived from photorec...

Over a family X of complete curves genus g, which gives the degeneration smooth curve into one with nodal singularities, we build moduli space is holomorphic SL(n,C) bundles over generic Xt in family, and equipped extra structure at nodes for family. This quotient by (C⁎)s on desingularization. Taking “maximal” built from glueing three-pointed spheres, obtain (C⁎)(3g−3)(n−1)-quotient (2g−2)-th ...