M
Martin Helmer
Researcher at Australian National University
Publications - 40
Citations - 192
Martin Helmer is an academic researcher from Australian National University. The author has contributed to research in topics: Euler characteristic & Toric variety. The author has an hindex of 8, co-authored 37 publications receiving 153 citations. Previous affiliations of Martin Helmer include University of Copenhagen & Queen's University.
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Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties
TL;DR: The algorithms are based on a new method for calculating the projective degrees of a rational map defined by a homogeneous ideal and are found to perform favourably compared to current algorithms for computing Chern-Schwartz-MacPherson classes, Segre classes and Euler characteristics.
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The Maximum Likelihood Degree of Toric Varieties
Carlos Améndola,Nathan Bliss,Isaac Burke,Courtney R. Gibbons,Martin Helmer,Serkan Hosten,Evan D. Nash,Jose Israel Rodriguez,Daniel Smolkin +8 more
TL;DR: The maximum likelihood (ML) degree of toric varieties, known as discrete exponential models in statistics, is studied, showing that the ML degree is equal to the degree of the toric variety for generic scalings, while it drops if and only if the scaling vector is in the locus of the principal A-determinant.
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Nearest points on toric varieties
Martin Helmer,Bernd Sturmfels +1 more
TL;DR: The primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.
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A direct algorithm to compute the topological Euler characteristic and Chern–Schwartz–MacPherson class of projective complete intersection varieties ☆
TL;DR: This algorithm complements existing algorithms by providing performance improvements in the computation of the Chern–Schwartz–MacPherson class and Euler characteristic for certain types of complete intersection subschemes of P n.
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Segre class computation and practical applications
TL;DR: In this paper, the Chow group of projective toric toric varieties has been used to compute intersection products in projective varieties, to determine algebraic multiplicity without working in local rings, and to test pairwise containment of subvarieties of a toric variety.