Abstracts

On the boundedness of elliptically fibered varieties Stefano Filipazzi

In this talk, we will survey some ideas to address the boundedness of varieties admitting an elliptic fibration. After introducing general ideas, we will discuss how they apply concretely to special classes of varieties: n-folds of Kodaira dimension n-1, and elliptic Calabi--Yau varieties. Part of this talk is based on current work in progress joint with C.D. Hacon and R. Svaldi.

Equations of secant varieties to Veronese varieties Giorgio Ottaviani

The secant varieties to Veronese varieties contain the symmetric tensors of bounded border (symmetric) rank. Apolarity theory was classically used to construct equations for such secant varieties. In a 2013 paper, joint with Landsberg, we introduced what is called today “nonabelian apolarity”, which gives some new equations, in cases when apolarity theory fails. Using projective techniques and Numerical Algebraic Geometry, we fill, in a joint work with Chiantini, some cases left open in that paper. The case of ternary sextics is particularly appealing, since a new invariant of degree 27, coming from second symmetric power of tangent bundle, marries into classical apolarity and it is enough to construct the equations to all secant varieties.

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The event is part of the series Topics in Birational Algebraic Geometry  

For more information please contact one of the organizers via e-mail:
Valentina Beorchia
Francesco Galuppi
Luigi Lombardi
Alex Massarenti
Luca Tasin
Stefano Urbinati