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Geometria

La quartica di Igusa e la mappa di Prym

Alessandro Verra


28-01-2021 - 14:30
modalitĂ  telematica

 

The Igusa quartic is a famous hypersurface of the complex projective 4-space, known for its ubiquity in algebraic geometry. A new 
case of ubiquity is presented, relating to the Prym map P in genus 6. P dominates the moduli space A of 5-dimensional p.p. abelian  
varieties. Its degree is 27 and its monodromy is the group of permutations preserving the configuration of 27 lines of the cubic surface. 
Other maps are associated to P with same monodromy and reflect related configurations.  Among these we study the map J:  D --- A, 
with general fibre the configuration of 'double sixes' of lines of the cubic surface. We show that J is the period map for the moduli space 
D of 30-nodal  quartic threefolds cutting twice a quadratic  section on the Igusa quartic. The rationality of D is also proven.
org: VERRA Alessandro

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