Computing Geometric Feature Sizes for Algebraic Manifolds

• We introduce numerical algebraic geometry methods for computing lower bounds on the reach, local feature size, and weak feature size of the real part of an equidimensional and smooth algebraic variety using the variety's defining polynomials as input. For the weak feature size, we also show that nonquadratic complete intersections generically have finitely many geometric bottlenecks, and we describe how to compute the weak feature size directly rather than a lower bound in this case. In all other cases, we describe additional computations that can be used to determine feature size values rather than lower bounds.

Ämnesord

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

bottlenecks

reach

numerical algebraic geometry

topological data analysis

weak feature size

Publikations- och innehållstyp

ref (ämneskategori)

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