Associated form morphism
Abstract
We study the geometry of the morphism between moduli spaces of hypersurfaces in $\mathbb P^{n-1}$ that sends a smooth hypersurface of degree $d+1$ to its associated hypersurface of degree $n(d-1)$. As a result, we obtain a compactification of the moduli space of smooth hypersurfaces such that the induced rational map from the standard GIT compactification often contracts the discriminant divisor.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2018
- DOI:
- 10.48550/arXiv.1807.02082
- arXiv:
- arXiv:1807.02082
- Bibcode:
- 2018arXiv180702082F
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Commutative Algebra;
- 14L24;
- 13A50;
- 13H10
- E-Print:
- 18 pages