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SUMMARY:Lian Duan (Colorado State University)
DTSTART:20210408T163000Z
DTEND:20210408T173000Z
DTSTAMP:20260422T055719Z
UID:SFUQNTAG/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUQNTAG/24/
 ">Bertini's theorem over finite field and Frobenius nonclassical varieties
 </a>\nby Lian Duan (Colorado State University) as part of SFU NT-AG semina
 r\n\n\nAbstract\nLet X be a smooth subvariety of $\\mathbb{P}^n$ defined o
 ver a field k. Suppose k is an infinite field\, then the classical theorem
  of Bertini asserts that X admits a smooth hyperplane section. However\, i
 f k is a finite field\, there are examples of X such that every hyperplane
  H in $\\mathbb{P}^n$ defined over k is tangent to X. One of the remedies 
 in this situation is to extending the ground field k to its finite extensi
 on\, and considering all the hyperplanes defined over the extension field.
  Then one can ask: Knowing the invariants of X (e.g. the degree of X)\, ho
 w  much one needs to extend k in order to guarantee at least one transvers
 e hyperplane section? In this talk we will report several results regardin
 g to this type of questions. We also want to talk about a special type of 
 varieties (Frobenius nonclassical varieties) that appear naturally in our 
 research. This is a joint work with Shamil Asgarli and Kuan-Wen Lai.\n
LOCATION:https://researchseminars.org/talk/SFUQNTAG/24/
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