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Mike Stillman: Investigating the geometry of curves and surfaces

Macaulay2 day February 03, 2009 - February 03, 2009

February 03, 2009 (11:00AM PST - 12:00PM PST)
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Abstract We show how to use Macaulay 2 to help investigate projective curves and surfaces. We will start out with a "mystery" curve: a curve given by equations in projective space. We then get to work understanding the curve. Along the way, we find the canonical embedding, and see how to compute sheaf cohomology in Macaulay 2. For the second example, we start with equations defining a surface, and once again, we try to understand the surface. We show how to compute invariants, intersection numbers, adjunction maps, exceptional lines, etc.
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