The Chow Ring of the Moduli Space of Curves of Genus 5

Izadi, Elham

doi:10.1007/978-1-4612-4264-2_10

Cited by 24 publications

(15 citation statements)

References 15 publications

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“…The intersection rings of M 1,1 and M 2 are computed in [6] and [15]. Even with rational coefficients the ring A * (M g ) is known only up to g = 5 (see [7] and [9]). …”

Section: Introductionmentioning

confidence: 99%

The Chow ring of the stack of cyclic covers of the projective line

Fulghesu¹,

Viviani²

2011

Ann. inst. Fourier

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“…The intersection rings of M 1,1 and M 2 are computed in [6] and [15]. Even with rational coefficients the ring A * (M g ) is known only up to g = 5 (see [7] and [9]). …”

Section: Introductionmentioning

confidence: 99%

The Chow ring of the stack of cyclic covers of the projective line

Fulghesu¹,

Viviani²

2011

Ann. inst. Fourier

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“…The complement of H 3,5 in the moduli space M 5 of smooth curves of genus five is isomorphic to the coarse moduli space of M PGL 4 (2, 2, 2) (see 1.2), whose Chow ring we can compute using Theorem 2.6. This enables us to reprove the following Theorem of Izadi (see [Iza95]).…”

Section: Moduli Of Curves Of Genus Fivementioning

confidence: 98%

“…Among the most relevant results in this area, we have the determination of the Chow ring of M 3 , the moduli space of stable curves of genus three, by Faber ([Fab90a]), and the computation by several different authors of the Chow ring of M g , the moduli space of smooth curves of genus g, for 2 ≤ g ≤ 9 ([Fab90b, Iza95,PV15b,CL21]).…”

Section: Introductionmentioning

confidence: 99%

Intersection theory on moduli of smooth complete intersections

Lorenzo¹

2022

Preprint

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We provide a general method for computing rational Chow rings of moduli of smooth complete intersections. We specialize this result in different ways: to compute the integral Picard group of the associated stack ; to obtain an explicit presentation of rational Chow rings of moduli of smooth complete intersections of codimension two; to prove old and new results on moduli of smooth curves of genus ≤ 5 and polarized K3 surfaces of degree ≤ 8.

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“…Mumford [Mum83,§ 8,p. 318] earlier described the Chow ring of M 2 , and Izadi [Iza95] later determined the Chow ring of M 5 . In genus up to five the Chow ring is all tautological, and of the form…”

Section: Introductionmentioning

confidence: 99%

The Chow ring of the moduli space of curves of genus six

Penev¹,

Vakil²

2015

Alg. Geom.

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We determine the Chow ring (with Q-coefficients) of M 6 by showing that all Chow classes are tautological. (In particular, all algebraic cohomology is tautological, and the natural map from Chow to cohomology is injective.) We stratify the moduli space into locally closed strata which are group quotients, and use a theorem of Vistoli to show that their Chow rings are generated by Chern classes of natural vector bundles. To demonstrate the utility of these methods, we also give quick derivations of the Chow groups of moduli spaces of curves of lower genus. The genus six case relies in addition on the particularly beautiful Brill-Noether theory in this case, and in particular on a rank five vector bundle "relativizing" a baby case of a celebrated construction of Mukai, which we interpret as a subbundle of the rank six vector bundle of quadrics cutting out the canonical curve.

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The Chow Ring of the Moduli Space of Curves of Genus 5

Cited by 24 publications

References 15 publications

The Chow ring of the stack of cyclic covers of the projective line

The Chow ring of the stack of cyclic covers of the projective line

Intersection theory on moduli of smooth complete intersections

The Chow ring of the moduli space of curves of genus six

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