Seminário Salomônico: Real Weierstrass points of a genus four smooth real algebraic curve.
Sexta-feira, 27 Maio 2016
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seminário Salomônico será na sexta-feira que vem, dia 27 de maio de 2016, às 14s+epsilon na sala 407 do bloco H do campus Gragoatá da UFF, em Niterói.
O Cristhian Garay (UFF) vai falar sobre o tema seguinte.
Título: Real Weierstrass points of a genus four smooth real algebraic curve.
Resumo: It is well-known that any genus four smooth complex algebraic curve has the same number of Weiertrass points (sixty). This is no longer true in the real case, in fact, we still do not know what is the maximal number of real Weierstrass points that a genus four smooth real algebraic curve may have.
In this talk I present two results towards the solution of this problem:
1. The first says that if the real curve in question C is generic and if F is (the map of) a resolution of singularities of its dual variety C*, then the number of real Weierstrass points of C is precisely the topological Euler characteristic of the pre-image under F of the real part of C*.
2. The second is the construction of genus four smooth real algebraic curves having thirty real Weierstrass points. This result uses methods from tropical geometry, and in particular sets the first non-trivial lower bound on the maximal number of real Weierstrass points that a genus four smooth real algebraic curve may have.