The Hodge conjecture for general Prym varieties

Biswas, Indranil; Paranjape, Kapil H.

doi:10.1090/s1056-3911-01-00303-4

Cited by 9 publications

(8 citation statements)

References 9 publications

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“…Remark 5.5. The property (D) and equality End(P ) = Z for general (not necessarily unramified) Prym varieties P of arbitrary smooth projective curves were proven in [1].…”

Section: Prym Varietiesmentioning

confidence: 97%

Hodge classes on certain hyperelliptic prymians

Zarhin¹

2012

Contemporary Mathematics

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“…Remark 5.5. The property (D) and equality End(P ) = Z for general (not necessarily unramified) Prym varieties P of arbitrary smooth projective curves were proven in [1].…”

Section: Prym Varietiesmentioning

confidence: 97%

Hodge classes on certain hyperelliptic prymians

Zarhin¹

2012

Contemporary Mathematics

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“…It is also known that, given a general étale double cover 𝐶 → 𝐶 ′ its Prym variety 𝑃(𝐶, 𝐶 ′ ) is simple (cf. [4] or [10] Proposition 3.4). Because 𝑃(𝐶, 𝐶 ′ ) is complementary to Jac 𝐶 ′ inside Jac 𝐶 (cf.…”

Section: Examplesmentioning

confidence: 99%

Surfaces close to the Severi lines

Conti

2022

Mathematische Nachrichten

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“…It is also known that, given a general étale double cover C → C ′ its Prym variety P (C, C ′ ) is simple (cf. [4] or [10] Proposition 3.4). Because P (C, C ′ ) is complementary to Jac C ′ inside Jac C (cf.…”

Section: Examplesmentioning

confidence: 99%

Surfaces close to the Severi lines

Conti

2019

Preprint

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Let X be a surface of general type with maximal Albanese dimension: if the Albanese morphism is composed with an involution, one has K 2 X ≥ 4χ(OX ) + 4(q − 2). We give a complete classification of surfaces for which equality holds for q(X) ≥ 3: these are surfaces whose canonical model is a double cover of a product elliptic surface branched over an ample divisor with at most negligible singularities which intersects twice the elliptic fibre.We also prove, in the same hypothesis, that a surface X with K 2 X = 4χ(OX ) + 4(q − 2) satisfies K 2 X ≥ 4χ(OX ) + 8(q − 2) and we give a characterization of surfaces for which the equality holds. These are surfaces whose canonical model is a double cover of an isotrivial smooth elliptic surface branched over an ample divisor with at most negligible singularities whose intersection with the elliptic fibre is 4.

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The Hodge conjecture for general Prym varieties

Cited by 9 publications

References 9 publications

Hodge classes on certain hyperelliptic prymians

Hodge classes on certain hyperelliptic prymians

Surfaces close to the Severi lines

Surfaces close to the Severi lines

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