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FOSICAV

Families of Subvarieties in Complex Algebraic Varieties

Total Cost €

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EC-Contrib. €

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Partnership

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Project "FOSICAV" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITA DEGLI STUDI DI ROMA TOR VERGATA 

Organization address
address: VIA CRACOVIA 50
city: ROMA
postcode: 133
website: www.uniroma2.it

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 Italy [IT]
 Project website http://www.mat.uniroma2.it/
 Total cost 180˙277 €
 EC max contribution 180˙277 € (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 2015-09-01   to  2017-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITA DEGLI STUDI DI ROMA TOR VERGATA IT (ROMA) coordinator 180˙277.00

Map

 Project objective

In relation with the study of both moduli and enumerative problems in complex algebraic geometry, we propose the geometric study of various families of subvarieties of certain complex algebraic varieties of small dimension, and mainly of families of (possibly singular) curves. The Severi varieties are a typical example: they parametrize curves of given degree and geometric genus in the projective plane; the general such curve has a prescribed number of ordinary double points and no further singularity.

Apart from exploring their dimensions, smoothness, and irreducibility properties, we have in mind to determine their Hilbert polynomials (which among other things encode their degrees, the latter being important enumerative invariants).

A central feature of our project is to conduct this analysis by degeneration: to study families of subvarieties in a given variety X, we let X degenerate and look at what happens in the limit. For instance, to study curves on a general K3 surface, we can let it degenerate to a union of projective planes, the dual graph of which is a triangulation of the real 2-sphere.

We shall consider the following kind of families of subvarieties: families of curves with prescribed invariants and singularities in surfaces (with special attention to the two cases of the projective plane, and of K3 surfaces), families of hyperplane sections with prescribed singularities of hypersurfaces in projective spaces, families of curves with a given genus in Calabi-Yau threefolds, and families of surfaces in the projective 3-space containing curves with unexpected singularities.

 Publications

year authors and title journal last update
List of publications.
2017 Ciro Ciliberto Thomas Dedieu
Limit Severi varieties of K3 surfaces degenerating to Platonic solids
published pages: , ISSN: , DOI:
2019-07-23
2017 Ciro Ciliberto Thomas Dedieu
On the irreducibility of Severi varieties on K3 surfaces
published pages: , ISSN: , DOI:
2019-07-23
2017 C. Ciliberto, Th. Dedieu, and E. Sernesi
Wahl maps and extensions of canonical curves and K3 surfaces
published pages: , ISSN: , DOI:
2019-07-23
2017 C. Ciliberto, Th. Dedieu, C. Galati, and A. L. Knutsen
Degenerations of Enriques surfaces and applications
published pages: , ISSN: , DOI:
2019-07-23

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