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pdfCarl MillerIs a separated etale birational morphism of integral schemes an open immersion?
pdfBhargav BhattAlternate Generalized Solution to: "Is a separated etale birational morphism of integral schemes an open immersion?"
pdfanonymousLet X be a smooth complex projective variety and |L| a linear system on X. Fix an ideal sheaf I in O_X. Suppose that the multiplier ideal sheaf J (X, lct(D) D) of a general divisor D in |L| is contained in I. It is known that for any divisor D' in |L|, we have J (X, lct(D) D') in I. But if there is a special element D' \in |L| such that lct(D') < lct(D), then is J (X, lct(D') D') still contained in I?
pdfanonymousI wonder if a generalization of the Fundamental Continuity Theorem for a single polynomial (see, e.g., Coolidge 1959, page 4) is valid for a system of two polynomials describing intersection points of two algebraic curves in the plane. This extension is meant in the following sense: we are given two systems of two polynomials of the same order in both variables, where the first .. (p,q) coefficients of the polynomials in the first system are zero. If the coefficients of the polynomials in the second system approach those in the first system as limits, k solutions of the second system will approach every solution of multiplicity k of the first system as a limit, whereas the remaining solutions of the second system will increase indefinitely.
Also see the following paper for an application of this fact: Click Here