Points, symbolic powers and a conjecture by G. V. Chudnovsky.

Date: 
Monday, February 15, 2016 - 4:00pm
Location: 
110 MSB
Speaker: 
Paolo Mantero, University of Arkansas

Abstract: What is the smallest possible degree of an equation passing at least m times through t given points in the complex projective space P^N? The answer is not known (except in few special cases), but the complex analyst G. 

​V. Chudnovsky in 1979 conjectured a lower bound, which is only known to hold for points in P^2, general points in P^3 and certain extremal configurations in P^N.

In this talk we will survey the evolving framework of conjectures and results around the above question, and prove Chudnovsky's conjecture for any set of very general points in P^N.

 

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