Zobrazeno 1 - 10
of 84
pro vyhledávání: '"Kapustka, Michal"'
We study the variety $\rm{VAPS}_G(q_2^3, 10)$ (resp. $\rm{VAPS}_G(q_3^2, 10)$), a Grassmannian compactification of the variety of finite schemes of length $10$ apolar to $q_{2}^3$ (resp. $q_3^2$), where $\{q_{n} = 0\}\subset \mathbb P^{n} $ is a smoo
Externí odkaz:
http://arxiv.org/abs/2409.13352
Autor:
Bernardara, Marcello, Fatighenti, Enrico, Kapustka, Grzegorz, Kapustka, Michał, Manivel, Laurent, Mongardi, Giovanni, Tanturri, Fabio
We study Fano fourfolds of K3 type with a conic bundle structure. We construct direct geometrical links between these fourfolds and hyperK\"ahler varieties. As a result we describe families of nodal surfaces that can be seen as generalisations of Kum
Externí odkaz:
http://arxiv.org/abs/2402.08528
Autor:
Kapustka, Grzegorz, Kapustka, Michał
We study twisted derived equivalences of hyper-K\"ahler fourfolds. We describe when two hyper-K\"ahler fourfolds of $K3^{[2]}$-type of Picard rank $1$ with isomorphic transcendental lattices are derived equivalent. Then we present new constructions o
Externí odkaz:
http://arxiv.org/abs/2312.14543
We study a correspondence between double EPW cubes and double EPW sextics, two families of polarized hyper-K\"ahler manifolds related to Gushel--Mukai fourfolds. We infer relations between these families in terms of Hodge structures and moduli spaces
Externí odkaz:
http://arxiv.org/abs/2202.00301
Autor:
Kapustka, Gregorz, Kapustka, Michał, Ranestad, Kristian, Schenck, Hal, Stillman, Mike, Yuan, Beihui
A quaternary quartic form, a quartic form in four variables, is the dual socle generator of an Artinian Gorenstein ring of codimension and regularity 4. We present a classification of quartic forms in terms of rank and powersum decompositions which c
Externí odkaz:
http://arxiv.org/abs/2111.05817
We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two projective bundle structures. Given a general hyperplane section on such a variety, we consider the zero loc
Externí odkaz:
http://arxiv.org/abs/2110.10475
Publikováno v:
Alg. Number Th. 18 (2024) 165-208
We study projective fourfolds of $K3^{[2]}$-type with a symplectic involution and the deformations of their quotients, called orbifolds of Nikulin types; they are IHS orbifolds. We compute the Riemann--Roch formula for Weil divisors on such orbifolds
Externí odkaz:
http://arxiv.org/abs/2104.09234
We show that the birationality class of a quadric surface bundle over $\mathbb{P}^2$ is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over $\mathbb{P}^2$ with discrimin
Externí odkaz:
http://arxiv.org/abs/2005.02092
Autor:
Kapustka, Michał, Rampazzo, Marco
We investigate a construction providing pairs of Calabi-Yau varieties described as zero loci of pushforwards of a hyperplane section on a roof as described by Kanemitsu. We discuss the implications of such construction at the level of Hodge equivalen
Externí odkaz:
http://arxiv.org/abs/2001.06385
Zariski decomposition plays an important role in the theory of algebraic surfaces due to many applications. For irreducible symplectic manifolds Boucksom provided a characterization of his divisorial Zariski decomposition in terms of the Beauville-Bo
Externí odkaz:
http://arxiv.org/abs/1911.03367