Symplectic enumeration

Levcovitz, Daniel; Vainsencher, Israel

doi:10.1007/s00574-011-0019-2

Cited by 5 publications

(3 citation statements)

References 5 publications

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“…(5, 0) 40 The values of N 2 (5, 0) and N 3 (7, 0) were already found in [LV11,Amo14]. One may try to get the number of smooth contact curves of some degree by throwing out the reducible ones.…”

Section: Final Remarksmentioning

confidence: 88%

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Enumeration of rational contact curves via torus actions

Muratore¹

2020

Preprint

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We prove that some Gromov-Witten numbers associated to rational contact (Legendrian) curves in any contact complex projective space with arbitrary incidence conditions are enumerative. Also, we use Bott formula on the Kontsevich space to find the exact value of those numbers. As an example, the numbers of rational contact curves of low degree in P 3 and P 5 are computed. The results are consistent with existing results.

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Section: Final Remarksmentioning

confidence: 88%

“…Despite their importance, enumerative invariants of contact curves are largely unknown, even for projective spaces. The first paper to address this problem is [LV11], where mainly planar curves in P 3 are analyzed. But the first work studying this problem using torus actions is Amorim's Ph.D. thesis [Amo14].…”

Section: Introductionmentioning

confidence: 99%

Enumeration of rational contact curves via torus actions

Muratore¹

2020

Preprint

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“…In particular, we found a complete list of characteristic numbers of contact curves. The enumeration of such curves, started by [LV11], was only partially known before. Our main result is thus the following theorem.…”

Section: Introductionmentioning

confidence: 99%

Effective computations of the Atiyah-Bott formula

Muratore,

Schneider

2021

Preprint

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We present an implementation of the Atiyah-Bott residue formula for M 0,m (P n , d). We use this implementation to compute a large number of Gromov-Witten invariants of genus 0, including characteristic numbers of rational curves on general complete intersections. We also compute some characteristic numbers of rational contact curves. Our computations confirm known predictions made by Mirror Symmetry. The code we developed for these computations is publicly available and can be used for other types of computations.

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Irreducible contact curves via graph stratification

Muratore¹

2023

Bulletin des Sciences Mathématiques

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Symplectic enumeration

Cited by 5 publications

References 5 publications

Enumeration of rational contact curves via torus actions

Enumeration of rational contact curves via torus actions

Effective computations of the Atiyah-Bott formula

Irreducible contact curves via graph stratification

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