On the ordinary and symbolic powers of fiber products
Hoang Viet Do, Hop D. Nguyen, Seyed Amin Seyed Fakhari
TL;DR
This paper provides exact formulas for the depth and regularity of symbolic and ordinary powers of fiber products of ideals, extending previous work and applicable across different characteristics.
Contribution
It offers the first complete characterization of depth and regularity for symbolic powers of fiber products, generalizing prior results to ordinary powers with explicit formulas.
Findings
Exact formulas for depth and regularity of symbolic powers
Characteristic-independent results for ordinary powers
Extension of previous joint work with Vu
Abstract
We completely determine the depth and regularity of symbolic powers of the fiber product of two homogeneous ideals in disjoint sets of variables, given knowledge of the symbolic powers of each factor. Generalizing previous joint work with Vu, we provide exact, characteristic-independent formulas for the depth and regularity of ordinary powers of such fiber products.
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Taxonomy
TopicsAdvanced Theoretical and Applied Studies in Material Sciences and Geometry