Surfaces on the Severi line

Barja, Miguel A.; Pardini, Rita; Stoppino, Lidia

doi:10.1016/j.matpur.2015.11.012

Cited by 18 publications

(12 citation statements)

References 11 publications

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“…Finally, [CF18, Table 3] contains three families of surfaces with K 2 X = 2 whose minimal models have K 2 = 4χ(O) = 4, so realizing the equality of Severi inequality. Indeed the description we obtain of their Albanese morphisms is coherent with the known characterization of these surfaces in [BPS16], [Zha14].…”

Section: Proofsupporting

confidence: 81%

Quotients of the square of a curve by a mixed action, further quotients and Albanese morphisms

Pignatelli

2019

Rev Mat Complut

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We study mixed surfaces, the minimal resolution S of the singularities of a quotient (C × C)/G of the square of a curve by a finite group of automorphisms that contains elements not preserving the factors. We study them through the further quotientsAs first application we prove that if the irregularity is at least 3, then S is also minimal. The result is sharp.The main result is a complete description of the Albanese morphism of S through a determined further quotient (C ×C)/G ′ that is anétale cover of the symmetric square of a curve. In particular, if the irregularity of S is at least 2, then S has maximal Albanese dimension.We apply our result to all the semi-isogenous mixed surfaces of maximal Albanese dimension constructed by Cancian and Frapporti, relating them with the other constructions of surfaces of general type having the same invariants in the literature.

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Section: Proofsupporting

confidence: 81%

Quotients of the square of a curve by a mixed action, further quotients and Albanese morphisms

Pignatelli

2019

Rev Mat Complut

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“…This conjecture was confirmed by Barja-Pardini-Stoppino [4] and Lu-Zuo [14] in characteristic zero independently.…”

Section: Introductionmentioning

confidence: 62%

Surfaces on the Severi line in positive characteristics

Gu,

Sun,

Zhou

2019

Preprint

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Let X be a minimal surface of general type over an algebraically closed field k of any characteristic. If the Albanese morphism a X : X → Alb X is generically finite onto its image, we formulate a constant c(X, L) ≥ 0 for a very ample line bundle L on Alb X such that c(X, L) = 0 if and only if dim Alb X = 2 and a X : X → Alb X is a double cover. A refined Severi inequalityis proved. Then we prove that K 2 X = 4χ(O X ) if and only if the canonical model of X is a flat double cover of an Abelian surface.

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“…In this section we give explicit examples of surfaces which satisfy equalities in Theorems 1.1 and 1.2, proving that all the inequalities are sharp. First we give an example of a surface satisfying equality in Theorem 1.1 for 𝑞 ≥ 3 (a characterization of the surfaces satisfying equality for 𝑞 = 2 is done in [1]).…”

Section: Examplesmentioning

confidence: 99%

“…In [1] there is a characterization of surfaces for which the inequality 1.2 is indeed an equality, namely these are surfaces whose canonical model is a double cover of its Albanese variety branched over an ample divisor with at most negligible singularities (in particular 𝑞 = 2). There are many generalizations of the Severi inequality; in particular Lu and Zuo have proved in [6] a similar inequality involving also the irregularity 𝑞: a surface of general type and maximal Albanese dimension satisfies 𝐾 : Lu and Zuo have proved that the canonical model of such a surface is a double cover of a smooth isotrivial elliptic surface branched over a divisor 𝑅 with at most negligible singularities.…”

Section: Introductionmentioning

confidence: 99%