Hyper-Kähler fourfolds and Grassmann geometry
By O. Debarre, Claire Voisin. 2009
98 citations recorded by the source corpus.
Abstract We construct a new 20-dimensional family of projective hyper-Kähler fourfolds and prove that they are deformation-equivalent to the second punctual Hilbert scheme of a K3 surface of genus 12.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3552f345964de88c736a06e9b8f4389e04a21d3b
How researchers see this paper
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In Geometry and Topology
- D. Huybrechts
- Emanuele Macrì
- P. Stellari
- Alexander Perry
- K. Hulek
- G. Sankaran
- V. Gritsenko
- E. Markman
In Mathematical Physics
- D. Huybrechts
- Emanuele Macrì
- P. Stellari
- K. Hulek
- G. Sankaran
- V. Gritsenko
- Alexander Perry
- E. Markman
Citations in the corpus
- Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spaces (2018, background): “ hand, we still do not know even a generic answer to Question 3.3 for GM fourfolds. 3.3. Debarre-Voisin manifolds. Also in this section, we assume char(K) = 0. DebarreVoisin manifolds were studied in [DV10] with the aim of constructing new examples of locally complete families of polarized hyperka¨h”
- A survey of Torelli and monodromy results for holomorphic-symplectic varieties (2011, background): “On the other hand, unirational components are those likely to admit explicit and very beautiful geometric descriptions [BD, DV , IR, Mu2, O’G4].”
- Derived categories of Gushel–Mukai varieties (2016, unknown): “here are some other Fano varieties which fit into the above story, i.e. whose derived category contains a K3 category. One example is provided by a hyperplane section of the Grassmannian Gr(3,10), see [13] for a discussion of related geometric questions and [30, Corollary 4.4] for the construction of”
- Double covers of EPW-sextics (2010, background): “Suppose that YA[3] 6= YA(3) i.”
- Chow Rings, Decomposition of the Diagonal, and the Topology of Families (2014, background): “are not obtained by the same construction, but they are not well understood except in a few cases, namely the four different families of hyper-Kähler fourfolds constructed in the papers [10], [29], [55], [77].”
- A global Torelli theorem for hyperkahler manifolds (2009, unknown): “y linear-algebraic calculation implies that the 2-form Ω :=√ ωJ+ −1 ωK is of Hodge type (2,0) on (M,I). This form is clearly closed and non-degenerate, hence it is a holomorphic symplectic form. 5See [DV] for an alternative approach to the same problem. – 11 – version9.2, March22, 2013 M.Verbitsky A”
- Moduli of K3 Surfaces and Irreducible Symplectic Manifolds (2010, background): “For an account of these results see also Voisin’s Bourbaki exposé [Vo1].”
- The integral Hodge conjecture for two-dimensional Calabi–Yau categories (2020, background): “These varieties were originally studied in [28] because of their role in the construction of a certain hyperkähler fourfold.”