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Tautological relations and the r -spin Witten conjecture

Carel Faber, Sergey Shadrin, Dimitri Zvonkine (2010)

Annales scientifiques de l'École Normale Supérieure

In [11], A. Givental introduced a group action on the space of Gromov–Witten potentials and proved its transitivity on the semi-simple potentials. In [24, 25], Y.-P. Lee showed, modulo certain results announced by C. Teleman, that this action respects the tautological relations in the cohomology ring of the moduli space ℳ ¯ g , n of stable pointed curves. Here we give a simpler proof of this result. In particular, it implies that in any semi-simple Gromov–Witten theory where arbitrary correlators can be...

Teorema de irreducibilidad para correspondencias algebraicas.

Eugenio Roanes (1980)

Revista Matemática Hispanoamericana

Sea T una correspondencia algebraica irreducible entre dos variedades proyectivas, V y V', sobre un cuerpo k algebraicamente cerrado y de característica cero. Sea W una subvariedad irreducible de V y W' = T{W} la transformada total de W en T. En [1] se estudia el problema de la conexión de W' y en [3] se estudia el problema de la irreducibilidad de la transformada total de W en correspondencias locales. La finalidad de este artículo es la de aprovechar los resultados de los dos trabajos citados,...

The automorphism group of M ¯ 0 , n

Andrea Bruno, Massimiliano Mella (2013)

Journal of the European Mathematical Society

The paper studies fiber type morphisms between moduli spaces of pointed rational curves. Via Kapranov’s description we are able to prove that the only such morphisms are forgetful maps. This allows us to show that the automorphism group of M ¯ 0 , n is the permutation group on n elements as soon as n ≥ 5 .

The degree of the secant variety and the join of monomial curves.

Kristian Ranestad (2006)

Collectanea Mathematica

A monomial curve is a curve parametrized by monomials. The degree of the secant variety of a monomial curve is given in terms of the sequence of exponents of the monomials defining the curve. Likewise, the degree of the join of two monomial curves is given in terms of the two sequences of exponents.

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