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INVLOCCY

Invariants of local Calabi-Yau 3-folds

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

INVLOCCY project word cloud

Explore the words cloud of the INVLOCCY project. It provides you a very rough idea of what is the project "INVLOCCY" about.

curve enumerative first zero perfect vertex ample questions physicists faber experts theory refinements formulae representation geometry physics gromov surfaces string theme refined explore geometers schools answer point supervisor branches location members prof relation equal housing sufficiently curves canonical algebraic certain bundle space relate topological contributions compute thomas section links calculations fano literature area utrecht moduli diverse count active leads gw contained play am class calculate counts outside relations witten central easiest me uu yau intend insertions calabi donaldson appearing mathematics world stable pairs invariants total university obtain folds correspondence counting expertise regime forms pair

Project "INVLOCCY" data sheet

The following table provides information about the project.

Coordinator	UNIVERSITEIT UTRECHT Organization address address: HEIDELBERGLAAN 8 city: UTRECHT postcode: 3584 CS website: www.uu.nl contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.
Coordinator Country	Netherlands [NL]
Project website	https://www.staff.science.uu.nl/
Total cost	165˙598 €
EC max contribution	165˙598 € (100%)
Programme	1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
Code Call	H2020-MSCA-IF-2014
Funding Scheme	MSCA-IF-EF-ST
Starting year	2015
Duration (year-month-day)	from 2015-06-01 to 2017-05-31

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	UNIVERSITEIT UTRECHT UNIVERSITEIT UTRECHT Organization address address: HEIDELBERGLAAN 8 city: UTRECHT postcode: 3584 CS website: www.uu.nl contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	NL (UTRECHT)	coordinator	165˙598.00

Map

Project objective

The study of Gromov-Witten (GW), Donaldson-Thomas, and stable pair invariants of Calabi-Yau 3-folds X forms an active area of research for geometers and physicists. These invariants play a central role in string theory and have relations with many branches of mathematics including number theory and representation theory. I am interested in questions of enumerative geometry on algebraic surfaces S. Invariants of the total space X of the canonical bundle over S can be used to answer classical enumerative questions on S. Two recent developments in stable pair theory are: (1) A better understanding of stable pairs on X not contained in the zero-section S. (2) Refinements of stable pair invariants. The first theme of my project is the study of stable pairs on X not contained in S in relation to enumerative questions. For Fano surfaces, GW invariants with sufficiently many point insertions are enumerative. By the GW/stable pairs correspondence these are equal to certain stable pair invariants of X. When the curve class is not sufficiently ample, the stable pair count may include stable pairs on X not contained in S. I propose to compute such contributions in order to obtain curve counts on S outside the ample regime. The second theme of my project is the study of refined stable pair invariants. I intend to relate the refined topological vertex appearing in the physics literature to refined invariants in the mathematics literature. Since stable pair invariants are often easiest to calculate of all the invariants of Calabi-Yau 3-folds, I expect this leads to new curve counting formulae and new calculations of refined invariants. Utrecht University, housing one of the leading schools in geometry in Europe, and Prof. Faber, one of the world's leading experts on moduli of curves, provide the perfect location and supervisor for this project. The diverse expertise of the members of the Mathematics (and Physics) Department at UU allow me to explore links with other areas.

Publications

List of publications.
year	authors and title	journal	last update
2017	M. Kool and L. GÃ¶ttsche Virtual refinements of the Vafa-Witten formula published pages: 36 pages, ISSN: , DOI:	preprint on arXiv, to be submitted to journal	2019-07-23
2016	M. Kool and R.P. Thomas (with an appendix by A. Pixton and D. Zagier) Stable pairs with descendents on local surfaces I: the vertical component published pages: 51 pages, ISSN: , DOI:	preprint on arXiv.org, accepted for publication in Pure and Applied Mathematics Quarterly	2019-07-23
2017	Amin Gholampour, Martijn Kool Rank 2 wall-crossing and the Serre correspondence published pages: 1599-1617, ISSN: 1022-1824, DOI: 10.1007/s00029-016-0293-3	Selecta Mathematica 23/2	2019-07-23
2017	Amin Gholampour, Martijn Kool, Benjamin Young Rank 2 Sheaves on Toric 3-Folds: Classical and Virtual Counts published pages: rnw302, ISSN: 1073-7928, DOI: 10.1093/imrn/rnw302	International Mathematics Research Notices	2019-07-23
2017	M. Kool and A. Gholampour Higher rank sheaves on threefolds and functional equations published pages: 33 pages, ISSN: , DOI:	arxiv.org, to be submitted to journal	2019-07-23

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The information about "INVLOCCY" are provided by the European Opendata Portal: CORDIS opendata.