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UID:ef2144f3f6c97bad939f042648ccaa27
CATEGORIES:Algebra Seminar
CREATED:20211207T102003
SUMMARY:Tevelev Degrees
LOCATION:Hill Center room 525
DESCRIPTION:<p>Let X be a non-singular complex projective variety. The virtual Tevelev 
 degree of X associated to (g,d,n) is the (virtual) degree of the forgetful 
 map from the Kontsevich moduli space M_g,n (X,d) of n-pointed stable maps t
 o X of genus g and degree d, to the product M_g,n × X^n .</p><p>Recent work
  of Lian and Pandharipande shows that this invariant is enumerative in many
  cases, that is, it is the number of degree-d maps from a fixed genus-g cur
 ve to X, that send n fixed points in the curve to n fixed points in X. I wi
 ll speak about a simple formula for this degree in terms of the (small) qua
 ntum cohomology ring of X. If X is a Grassmann variety (or more generally, 
 a cominuscule flag variety) then the virtual Tevelev degrees of X can be ex
 pressed in terms of the (real) eigenvalues of a symmetric endomorphism of t
 he quantum cohomology ring. <br />If X is a complete intersection of low de
 gree compared to its dimension, then the virtual Tevelev degrees of X are g
 iven by an explicit product formula. I will do my best to keep this talk st
 udent-friendly, so the most of it will be about explaining the ingredients 
 of this abstract. <br />The results are joint work with Rahul Pandharipande
 .</p>
CONTACT:Anders Buch (Rutgers University)
DTSTAMP:20260827T141939
DTSTART;TZID=America/New_York:20211208T110000
DTEND;TZID=America/New_York:20211208T120000
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