On the Chern Number of an Ideal
Mousumi Mandal, J. K. Verma
TL;DR
This paper proves Vasconcelos's negativity conjecture for the Chern number in specific unmixed quotients of regular local rings by explicitly calculating Hilbert polynomials of parameter-generated ideals.
Contribution
It provides a proof of the negativity conjecture for the Chern number in certain algebraic structures through explicit Hilbert polynomial calculations.
Findings
Confirmed the negativity conjecture for the Chern number in specified cases
Explicitly computed Hilbert polynomials for parameter ideals
Established a method for analyzing Chern numbers in regular local rings
Abstract
We settle the negativity conjecture of Vasconcelos for the Chern number of an ideal in certain unmixed quotients of regular local rings by explicit calculation of the Hilbert polynomials of all ideals generated by systems of parameters.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic structures and combinatorial models