Algebraic Cycles and Intersections of 2 Quadrics

Laterveer, Robert

doi:10.1007/s00009-021-01787-5

Cited by 9 publications

(14 citation statements)

References 34 publications

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“…In dimension two, a smooth quartic in P 3 has an MCK decomposition, but a very general surface of degree ≥ 7 in P 3 should not have one [15,Proposition 3.4]. For a discussion in greater detail, and further examples of varieties with an MCK decomposition, the reader may check [51, Section 8], as well as [55], [52], [16], [29], [30], [31], [32], [33], [34], [35], [36], [37], [15], [38], [39], [40] We say that Y → B has the Franchetta property if Y → B has the Franchetta property in codimension j for all j.…”

Section: Mck Decompositionmentioning

confidence: 99%

Some Motivic Properties of Gushel-Mukai Sixfolds

Bolognesi¹,

Laterveer²

2022

Preprint

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Gushel-Mukai sixfolds are an important class of so-called Fano-K3 varieties. In this paper we show that they admit a multiplicative Chow-Künneth decomposition modulo algebraic equivalence and that they have the Franchetta property. As side results, we show that double EPW sextics and cubes have the Franchetta property, modulo algebraic equivalence, and some vanishing results for the Chow ring of Gushel-Mukai sixfolds.

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Section: Mck Decompositionmentioning

confidence: 99%

Some Motivic Properties of Gushel-Mukai Sixfolds

Bolognesi¹,

Laterveer²

2022

Preprint

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“…For more detailed discussion, and examples of varieties with an MCK decomposition, we refer to [42,Section 8], as well as [48], [43], [14], [22], [32], [23], [24], [27], [30], [13]. We say that Y → B has the Franchetta property if Y → B has the Franchetta property in codimension j for all j.…”

Section: Preliminariesmentioning

confidence: 99%

Some new Fano varieties with a multiplicative Chow-Künneth decomposition

Laterveer¹

2021

Preprint

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“…To give an idea: hyperelliptic curves have an MCK decomposition [40,Example 8.16], but the very general curve of genus ≥ 3 does not have an MCK decomposition [11,Example 2.3]. For more detailed discussion, and examples of varieties with an MCK decomposition, we refer to [40,Section 8], as well as [48], [41], [12], [25], [26], [27], [28], [29], [30], [31], [11], [35].…”

Section: It Is Expected That For Any X With An Mck Decomposition One Hasmentioning

confidence: 99%