On threefolds isogenous to a product of curves

Frapporti, Davide; Gleissner, Christian

doi:10.1016/j.jalgebra.2016.06.034

Cited by 8 publications

(8 citation statements)

References 16 publications

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“…Remark 5.12. The Chevalley-Weil formula given in (5.11) is not in the original form of [CW34], but in the form of [FG15], theorem 1.11. 2 Using (5.11), we see that…”

Section: Proof See [Cat92] Sectionmentioning

confidence: 99%

G-marked moduli spaces

2018

Commun. Contemp. Math.

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The aim of this paper is to investigate the closed subschemes of moduli spaces corresponding to projective varieties which admit an effective action by a given finite group G. To achieve this, we introduce the moduli functorGorenstein canonical models with Hilbert polynomial h, and prove the existence of M h [G], the coarse moduli scheme for M G h . Then we show that M h [G] has a proper and finite morphism onto M h so that its image M h (G) is a closed subscheme. In the end we obtain the canonical representation type decomposition D h [G] of M h [G] and use D h [G] to study the structure of M h [G].

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“…Remark 5.12. The Chevalley-Weil formula given in (5.11) is not in the original form of [CW34], but in the form of [FG15], theorem 1.11. 2 Using (5.11), we see that…”

Section: Proof See [Cat92] Sectionmentioning

confidence: 99%

G-marked moduli spaces

2018

Commun. Contemp. Math.

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“…Similarly, the quotient of the product by G is called of unmixed or mixed type, respectively. In this paper, unless otherwise stated, we will consider the mixed case (see [FG16] for the unmixed).…”

Section: Generalitiesmentioning

confidence: 99%

“…In particular, surfaces isogenous to a product with holomorphic Euler-Poincaré-characteristic χ(O X ) = 1 were completely classified (see [BCG08,CP09,Pe10] et al). However, a systematic treatment of the higher-dimensional case was still missing until the author, in collaboration with Davide Frapporti [FG16], started to study these varieties in dimension three under the assumption that the action is unmixed i.e. each automorphism acts diagonally:…”

Section: Introductionmentioning

confidence: 99%

Mixed Threefolds Isogenous to a Product

Gleissner¹

2017

Preprint

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In this paper we study threefolds isogenous to a product of mixed type i.e. quotients of a product of three compact Riemann surfaces C i of genus at least two by the action of a finite group G, which is free, but not diagonal. In particular, we are interested in the systematic construction and classification of these varieties. Our main result is the full classification of threefolds isogenous to a product of mixed type with χ(O X ) = −1 assuming that any automorphism in G, which restricts to the trivial element in Aut(C i ) for some C i , is the identity on the product. Since the holomorphic Euler-Poincaré-characteristic of a smooth threefold of general type with ample canonical class is always negative, these examples lie on the boundary, in the sense of threefold geography. To achieve our result we use techniques from computational group theory. Indeed, we develop a MAGMA algorithm to classify these threefolds for any given value of χ(O X ).

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“…[FPP16], [MZ18], [CFGP19] and the references therein), of totally geodesic subvarieties of M g [EMMW20], and also in the classification of higher dimensional varieties (see e.g. [Cat15], [FG16], [Cat17], [LLR20]). Similar loci in the moduli space of higher dimensional varieties have been studied in [Li18].…”

Section: Introductionmentioning

confidence: 99%