منابع مشابه
Frobenius Morphisms of Noncommutative Blowups
We define the Frobenius morphism of certain class of noncommutative blowups in positive characteristic. Thanks to a nice property of the class, the defined morphism is always flat. Therefore we say that the noncommutative blowups in this class are Kunz regular. One of such blowups is the one associated to a regular Galois alteration. From de Jong’s theorem, we see that for every variety over an...
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In this note we study the fibers of a rational map from an algebraic point of view. We begin by describing two interpretations of the word ‘fiber’. Let S = k[x0, . . . , xn] be a polynomial ring over an infinite field k, I ⊂ S an ideal generated by an r+1-dimensional vector space W of forms of the same degree, and φ the associated rational map P → P = P(W ). We will use this notation throughout...
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The harmonic morphisms φ : M → Nn are studied using the methods of the moving frame and exterior differential systems and three main results are achieved. The first result is a local structure theorem for such maps in the case that φ is a submersion, in particular, a normal form is found for all such φ once the metric on the target manifold N is specified. The second result is a finiteness theo...
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Affectionately dedicated to Mel Hochster, who has been an inspiration to us for many years, on the occasion of his 65th birthday. Abstract We study the fibers of projective morphisms and rational maps. We characterize the analytic spread of a homogeneous ideal through properties of its syzygy matrix. Powers of linearly presented ideals need not be linearly presented, but we identify a weaker li...
متن کاملSingularities Appearing on Generic Fibers of Morphisms between Smooth Schemes
I give various criteria for singularities to appear on geometric generic fibers of morphism between smooth schemes in positive characteristics. This involves local fundamental groups, jacobian ideals, projective dimension, tangent and cotangent sheaves, and the effect of Frobenius. As an application, I determine which rational double points do appear on geometric generic fibers.
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 2016
ISSN: 0027-7630,2152-6842
DOI: 10.1017/nmj.2016.34