358 research outputs found
A simple limit for slope instability
Ross and Thomas have shown that subschemes can K-destabilise polarised
varieties, yielding a notion known as slope (in)stability for varieties. Here
we describe a special situation in which slope instability for varieties (for
example of general type) corresponds to a slope instability type condition for
certain bundles, making the computations almost trivial.Comment: 11 page
On Clifford's theorem for singular curves
Let C be a 2-connected Gorenstein curve either reduced or contained in a
smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim
scheme such that the space H^0(C, I_S K_C) contains a generically invertible
section). Under some general assumptions on S or C we show that h^0(C, I_S K_C)
<= p_a(C) - deg (S)/2 and if equality holds then either S is trivial, or C is
honestly hyperelliptic or 3-disconnected. As a corollary we give a
generalization of Clifford's theorem for reduced curves
The canonical ring of a 3-connected curve
Let C be a projective curve either reduced with planar singularities or
contained in a smooth algebraic surface. We show that the canonical ring R(C,
\omega_C)= \oplus_{k \geq 0} H^0(C, \omega_C^k is generated in degree 1 if C is
3-connected and not (honestly) hyperelliptic; we show moreover that R(C,
L)=\oplus_{k \geq 0} H^0(C,L^k)$ is generated in degree 1 if C is reduced with
planar singularities and L is an invertible sheaf such that deg L_{|B} \geq
2p_a(B)+1 for every B \subseteq C
It All Begins with One Case
The article discusses the seven roles that pharmacists must fulfil to become a seven star pharmacist as categorised in the WHO report 'Preparing the Future Pharmacist'. The roles of caregiver, decision maker, communicator, leader, manager, lifelong learner, and teacher are considered essential minimum common expectations of pharmacists by health systems worldwide
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