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Homogeneous polynomials with isomorphic Milnor algebras

Imran Ahmed (2010)

Czechoslovak Mathematical Journal

We recall first Mather's Lemma providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. We show that two homogeneous polynomials having isomorphic Milnor algebras are right-equivalent.

Homological Mirror Symmetry for manifolds of general type

Anton Kapustin, Ludmil Katzarkov, Dmitri Orlov, Mirroslav Yotov (2009)

Open Mathematics

In this paper we outline the foundations of Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical prospectives are considered.

Homological projective duality

Alexander Kuznetsov (2007)

Publications Mathématiques de l'IHÉS

We introduce a notion of homological projective duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are homologically projectively dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an equivalent nontrivial component. In particular, it follows that triangulated categories of singularities of these sections are...

Hyperbolic geometry and moduli of real cubic surfaces

Daniel Allcock, James A. Carlson, Domingo Toledo (2010)

Annales scientifiques de l'École Normale Supérieure

Let ℳ 0 ℝ be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space H 4 and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in PO ( 4 , 1 ) . We also derive several new and several old results on the topology of ℳ 0 ℝ ....

Hyperdéterminant d’un S L 2 -homomorphisme

Jean Vallès (2008)

Annales mathématiques Blaise Pascal

Etant donnés A 1 , ⋯ , A s ( s ≥ 3 ) des S L 2 ( ℂ ) -modules non triviaux de dimensions respectives n 1 + 1 ≥ ⋯ ≥ n s + 1 (avec n 1 = n 2 + ⋯ + n s ) et φ ∈ ℒ ( A 2 ⊗ ⋯ ⊗ A s , A 1 * ) un S L 2 ( ℂ ) -homomorphisme, nous montrons que l’hyperdéterminant de φ est nul sauf si les modules A i sont irréductibles et si l’homomorphisme est la multiplication des polynômes homogènes à deux variables.

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