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The moduli space of totally marked degree two rational maps

Anupam Bhatnagar (2015)

Acta Arithmetica

A rational map ϕ: ℙ¹ → ℙ¹ along with an ordered list of fixed and critical points is called a totally marked rational map. The space R a t ₂ t m of totally marked degree two rational maps can be parametrized by an affine open subset of (ℙ¹)⁵. We consider the natural action of SL₂ on R a t ₂ t m induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space R a t ₂ t m / S L ₂ exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over ℤ[1/2].

Troesch complexes and extensions of strict polynomial functors

Antoine Touzé (2012)

Annales scientifiques de l'École Normale Supérieure

We develop a new approach of extension calculus in the category of strict polynomial functors, based on Troesch complexes. We obtain new short elementary proofs of numerous classical Ext -computations as well as new results. In particular, we get a cohomological version of the “fundamental theorems” from classical invariant theory for  G L n for  n big enough (and we give a conjecture for smaller values of  n ). We also study the “twisting spectral sequence” E s , t ( F , G , r ) converging to the extension groups Ext 𝒫 𝕜 * ( F ( r ) , G ( r ) ) between the...

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Andrew R. Linshaw, Gerald W. Schwarz, Bailin Song (0)

Annales de l’institut Fourier

Currently displaying 121 – 140 of 144