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SUMMARY:Yongnam Lee (Korea Advanced Institute of Science and Technology)
DTSTART:20211007T110000Z
DTEND:20211007T120000Z
DTSTAMP:20260423T053137Z
UID:ZAG/153
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/153/">Do
 minant rational maps from a very general hypersurface</a>\nby Yongnam Lee 
 (Korea Advanced Institute of Science and Technology) as part of ZAG (Zoom 
 Algebraic Geometry) seminar\n\n\nAbstract\nThere has been recent interest 
 in studying measures of irrationality for hypersurfaces $X$ of high degree
  in $\\mathbb P^{n+1}$. The degree of irrationality of $X$ is defined as t
 he minimal degree of dominant rational maps from $X$ to $\\mathbb P^n$. It
  is known that the degree of irrationality of $X$ is $d-1$ if $X$ is a ver
 y general hypersurface of degree $d\\ge 2n+1$. In this talk\, from a diffe
 rent point of view we will discuss dominant rational maps of finite degree
  from a very general hypersurface $X$ of degree $d\\ge n+3$ in $\\mathbb P
 ^{n+1}$ to any smooth projective variety $Z$. The finite theorem states th
 at these form a finite set\, up to birational equivalence of $Z$\, if $Z$ 
 is a variety of general type. It is an interesting question to determine $
 Z$ when $Z$ is not birational to $X$. It is conjecturally expected that $Z
 $ is rationally connected if $X$ is a very general hypersurface of degree 
 $d\\ge n+3$. In this talk\, I will present some partial results for this e
 xpectation. This talk combines the joint work with Gian Pietro Pirola and 
 the joint work with De-Qi Zhang.\n
LOCATION:https://researchseminars.org/talk/ZAG/153/
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