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The Lefschetz standard conjectures for IHSMs of generalized Kummer deformation type in certain degrees
For a projective 2 n -dimensional irreducible holomorphic symplectic manifold Y of generalized Kummer deformation type and j the smallest prime number...
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Lefschetz Fixed Point Theorems for Correspondences
The classical Lefschetz fixed point theorem states that the number of fixed points, counted with multiplicity ± 1, of a smooth map f from a manifold...
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On the tropical Lefschetz–Hopf trace formula
In this follow-up to Rau (The tropical Poincaré–Hopf theorem, 2020. ar**v:2007.11642 ), our main result is a tropical Lefschetz–Hopf trace formula for...
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Waring problems and the Lefschetz properties
We study three variations of the Waring problem for homogeneous polynomials, concerning the Waring rank, the border rank and the cactus rank of a...
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The Lefschetz defect of Fano varieties
Smooth, complex Fano varieties are a very natural class of projective varieties, and have been intensively studied both classically and in recent...
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On the Lefschetz Zeta Function for a Class of Toral Maps
In the present article we study the periodic structure of a class of maps on the n -dimensional torus such that the eigenvalues of the induced map on...
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Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces
We generalize and extend the Conley-Morse-Forman theory for combinatorial multivector fields introduced in Mrozek (Found Comput Math 17(6):1585–1633,...
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Hodge similarities, algebraic classes, and Kuga–Satake varieties
We introduce in this paper the notion of Hodge similarities of transcendental lattices of hyperkähler manifolds and investigate the Hodge conjecture...
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Adaptive Parameter Alternating Direction Algorithm for Centrosymmetric Solutions of a Class of Generalized Coupled Sylvester-transpose Matrix Equations
We propose an adaptive parameter alternating direction algorithm to solve a class of generalized coupled Sylvester-transpose matrix equations over...
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Remarks on Some Compact Symplectic Solvmanifolds
We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients M = Γ G of a simply-connected solvable Lie group G ...
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Unchaining surgery and topology of symplectic 4-manifolds
We study a symplectic surgery operation we call unchaining , which effectively reduces the second Betti number and the symplectic Kodaira dimension at...
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The Generalized Roof F(1, 2,n): Hodge Structures and Derived Categories
We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two...
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Compatible relative open books on relative contact pairs via generalized square bridge diagrams
Using square bridge position, Akbulut-Ozbagci and later Arikan gave algorithms both of which construct an explicit compatible open book decomposition...
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Hyper–Kähler Manifolds of Generalized Kummer Type and the Kuga–Satake Correspondence
We first describe the construction of the Kuga–Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kähler type. We...
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Chapter 3 Estimate of the Number of Zeros of Abelian Integrals
In the study of the weak Hilbert’s 16th problem by using Abelian integrals, it is crucial to estimate the number of zeros of them. In this chapter,...
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