THIS THESIS DESCRIBES THE GRADED MINIMAL FREE RESOLUTION OF A PRODUCT OF IDEALS, EACH GENERATED BY LINEAR FORMS. IT ALSO STUDIES A PHENOMENON OF LINEARIZATION OF THE RESOLUTION OF AN ARBITRARY IDEAL, UPON MULTIPLICATION BY SUFFICIENTLY MANY IDEALS OF GENERIC POINTS IN PROJECTIVE SPACE. FURTHER, IT PROVIDES A CLASS OF BASE SETS OF THE ALGEBRAIC MATROID OF THE DETERMINANTAL VARIETY AND CONJECTURES THAT THESE COMPLETELY CHARACTERIZE THE MATROID. FINALLY, IT PROVIDES DETERMINANTAL CONDITIONS FOR HOMOMORPHIC SENSING, A PROBLEM THAT STUDIES THE UNIQUENESS OF IMAGES OF POINTS IN A VECTOR SUBSPACE UNDER A FINITE SET OF LINEAR TRANSFORMATIONS.
On resolutions of ideals associated to subspace arrangements and the algebraic matroid of the determinantal variety
TSAKIRIS, MANOLIS
2021-04-08
Abstract
THIS THESIS DESCRIBES THE GRADED MINIMAL FREE RESOLUTION OF A PRODUCT OF IDEALS, EACH GENERATED BY LINEAR FORMS. IT ALSO STUDIES A PHENOMENON OF LINEARIZATION OF THE RESOLUTION OF AN ARBITRARY IDEAL, UPON MULTIPLICATION BY SUFFICIENTLY MANY IDEALS OF GENERIC POINTS IN PROJECTIVE SPACE. FURTHER, IT PROVIDES A CLASS OF BASE SETS OF THE ALGEBRAIC MATROID OF THE DETERMINANTAL VARIETY AND CONJECTURES THAT THESE COMPLETELY CHARACTERIZE THE MATROID. FINALLY, IT PROVIDES DETERMINANTAL CONDITIONS FOR HOMOMORPHIC SENSING, A PROBLEM THAT STUDIES THE UNIQUENESS OF IMAGES OF POINTS IN A VECTOR SUBSPACE UNDER A FINITE SET OF LINEAR TRANSFORMATIONS.File | Dimensione | Formato | |
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phdunige_4449843.pdf
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