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SUMMARY:Victor Batyrev (University of Tübingen)
DTSTART:20210611T120000Z
DTEND:20210611T130000Z
DTSTAMP:20260423T023936Z
UID:ToricDeg/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ToricDeg/1/"
 >Variations on the theme of classical discriminant</a>\nby Victor Batyrev 
 (University of Tübingen) as part of Toric Degenerations\n\n\nAbstract\nTh
 e classical discriminant $\\Delta_n(f)$ of a degree $n$ polynomial $f(x)$ 
 is an irreducible homogeneous polynomial of degree $2n-2$ on the coefficie
 nts $a_0\, \\ldots\, a_n$ of $f$ that vanishes if and only if  $f$ has a m
 ultiple zero. I will explain a tropical proof of the theorem of Gelfand\, 
 Kapranov and Zelevinsky (1990) that identifies the Newton polytope  $P_n$ 
 of $\\Delta_n$ with a $(n-1)$-dimensional combinatorial cube obtained from
  the classical root system of type $A_{n-1}$. Recently Mikhalkin and Tsikh
  (2017) discovered a nice factorization property for truncations of $\\Del
 ta_n$ with respect to facets $\\Gamma_i$ of $P_n$ containing the vertex $v
 _0  \\in P_n$ corresponding to the monomial $a_1^2 \\cdots a_{n-1}^2 \\in 
 \\Delta_n$. I will give a GKZ-proof of this property and show its connecti
 on to the boundary stata in the $(n-1)$-dimensional toric Losev-Manin modu
 li space $\\overline{L_n}$. Some variations on the above statements will b
 e discussed in connection to the toric moduli space associated with the ro
 ot system of type $B_n$ and the mirror symmetry for $3$-dimensional cyclic
  quotient singularities ${\\mathbb C}^3/\\mu_{2n+1}$.\n
LOCATION:https://researchseminars.org/talk/ToricDeg/1/
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