Based on the Cayley, Grothendieck, Knudsen Mumford theory of determinants we extend the CM polarization to the Hilbert scheme. The Baum Fulton Macpherson GRR Theorem enables us to show that on any flat, proper, local complete intersection family the restriction of the extension and the original CM sheaf are isomorphic (under a mild hypothesis on the base). As a consequence the CM stability impl...

Let f:X⟶Y be a genuinely ramified map between irreducible smooth projective curves defined over an algebraically closed field. P branch data on Y such that P(y) and Bf(y), where Bf is for f, are linearly disjoint every y∈Y. Further assume either tame or f Galois. Then the pullback, by of any stable parabolic bundle with respect to actually X f∗P.

Based on the Cayley, Grothendieck, Knudsen Mumford theory of determinants we extend the CM polarisation to the Hilbert scheme. The Baum Fulton Macpherson GRR Theorem enables us to show that on any flat, proper, local complete intersection family the restriction of the extension and the original CM sheaf are isomorphic (under a mild hypothesis on the base). As a consequence the CM stability impl...

Based on the Cayley, Grothendieck, Knudsen Mumford theory of determinants we extend the CM polarisation to the Hilbert scheme. The Baum Fulton Macpherson GRR Theorem enables us to show that on any flat, proper, local complete intersection family the restriction of the extension and the original CM sheaf are isomorphic (under a mild hypothesis on the base). As a consequence the CM stability impl...

in this paper, new definitions of $l$-fuzzy closure operator, $l$-fuzzy interior operator, $l$-fuzzy remote neighborhood system, $l$-fuzzy neighborhood system and $l$-fuzzy quasi-coincident neighborhood system are proposed. it is proved that the category of $l$-fuzzy closure spaces, the category of $l$-fuzzy interior spaces, the category of $l$-fuzzy remote neighborhood spaces, the category of ...

We shall give an explicit pair of birational projective Calabi–Yau threefolds which are rigid, non-homeomorphic, but are connected by projective flat deformation over some connected base scheme. 0. Introduction A Calabi–Yau manifold is a compact Kähler simply-connected manifold with a nowhere vanishing global n-form but no global i-from with 0 < i < n = dimX . By Kodaira’s criterion, it is proj...

This paper considers some extensions of the notion filter to quantale-valued context, including saturated prefilter, ?-filter and bounded prefilter. The question is whether these constructions give rise monads on category sets. It shown that answer depends structure quantale. Specifically, if quantale unit interval equipped with a continuous t-norm, then only implication operator corresponding ...

In this paper we study some properties of GC -projective, injective and flat modules, where C is a semidualizing module and we discuss some connections between GC -projective, injective and flat modules , and we consider these properties under change of rings such that completions of rings, Morita equivalences and the localizations.

We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the qu...