degeneracy loci
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Author(s):  
Vladimiro Benedetti ◽  
Sara Angela Filippini ◽  
Laurent Manivel ◽  
Fabio Tanturri

2020 ◽  
Vol 156 (8) ◽  
pp. 1623-1663
Author(s):  
Amin Gholampour ◽  
Richard P. Thomas

We express nested Hilbert schemes of points and curves on a smooth projective surface as ‘virtual resolutions’ of degeneracy loci of maps of vector bundles on smooth ambient spaces. We show how to modify the resulting obstruction theories to produce the virtual cycles of Vafa–Witten theory and other sheaf-counting problems. The result is an effective way of calculating invariants (VW, SW, local PT and local DT) via Thom–Porteous-like Chern class formulae.


Author(s):  
Vladimiro Benedetti ◽  
Laurent Manivel ◽  
Fabio Tanturri

2020 ◽  
Vol 2 (3) ◽  
pp. 633-665 ◽  
Author(s):  
Amin Gholampour ◽  
Richard P. Thomas

2019 ◽  
Vol 2019 (748) ◽  
pp. 241-268 ◽  
Author(s):  
Atanas Iliev ◽  
Grzegorz Kapustka ◽  
Michał Kapustka ◽  
Kristian Ranestad

Abstract We construct a new 20-dimensional family of projective six-dimensional irreducible holomorphic symplectic manifolds. The elements of this family are deformation equivalent with the Hilbert scheme of three points on a K3 surface and are constructed as natural double covers of special codimension-three subvarieties of the Grassmannian G(3,6) . These codimension-three subvarieties are defined as Lagrangian degeneracy loci and their construction is parallel to that of EPW sextics, we call them the EPW cubes. As a consequence we prove that the moduli space of polarized IHS sixfolds of K3 -type, Beauville–Bogomolov degree 4 and divisibility 2 is unirational.


10.37236/8023 ◽  
2018 ◽  
Vol 25 (4) ◽  
Author(s):  
Jordan Lambert

Theta-vexillary signed permutations are elements in the hyperoctahedral group that index certain classes of degeneracy loci of type B and C. These permutations are described using triples of $s$-tuples of integers subject to specific conditions. The objective of this work is to present different characterizations of theta-vexillary signed permutations, describing them in terms of corners in the Rothe diagram and pattern avoidance.


2018 ◽  
Vol 2020 (24) ◽  
pp. 9887-9932 ◽  
Author(s):  
Vladimiro Benedetti ◽  
Sara Angela Filippini ◽  
Laurent Manivel ◽  
Fabio Tanturri

Abstract In [3] we introduced orbital degeneracy loci as generalizations of degeneracy loci of morphisms between vector bundles. Orbital degeneracy loci can be constructed from any stable subvariety of a representation of an algebraic group. In this paper we show that their canonical bundles can be conveniently controlled in the case where the affine coordinate ring of the subvariety is Gorenstein. We then study in a systematic way the subvarieties obtained as orbit closures in representations with finitely many orbits, and we determine the canonical bundles of the corresponding orbital degeneracy loci in the Gorenstein cases. Applications are given to the construction of low-dimensional varieties with negative or trivial canonical bundle.


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