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We will give a sharp bound for the regularity index of arbitrary fat points in P 3 which generalizes Segre bound for the regularity of fat points in general position.
We study additive submonoids M of N n consisting of the solutions of a homogeneous linear diophantine equation with integer coefficients. Surprisingly, not very much is known about the structure of M . M is a Krull monoid which, however, cannot be realized as a multiplicative monoid of a Krull...
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In this paper, we show that if a finitely presented group G is the fundamental group of a finite fake surface in which the link of any vertex is not homeomorphic to the 1-skeleton of a tetrahedron, then there is a finite 2-complex K with π 1 ( K )≅ G and whose universal cover K̃ has the...
Let P 1 ,…, P r be r general points of the projective plane over an algebraically closed field. Consider the linear system L of plane curves of degree d passing through each point P i with a prescribed multiplicity m i . It is still an open problem to know whether or not L has the expected...
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