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SUMMARY:Degenerations of Nikulin surfaces and moduli of curves
DTSTART;VALUE=DATE-TIME:20161125T102000Z
DTEND;VALUE=DATE-TIME:20161125T111000Z
DTSTAMP;VALUE=DATE-TIME:20191118T160603Z
UID:indico-contribution-1242-50@indico.math.cnrs.fr
DESCRIPTION:Speakers: Andreas Knutsen ()\nNikulin surfaces are surfaces ar
ising as quotiens of K3 surfaces by a symplectic involution. They have eig
ht nodes (arising from the eight fixed points of the involution)\, and the
ir desingularizations are smooth K3 surfaces with eight $(-2)$-curves whos
e sum is $2$-divisible in the Picard group. A particular feature is that t
heir smooth hyperplane sections carry a nontrivial $2$-torsion element in
their Picard group that is induced from a line bundle on the surface. Ther
e is therefore a natural moduli map from the space $P_g$ of pairs $(S\,C)$
where $S$ is a Nikulin surface and $C$ is a smooth genus $g$ hyperplane s
ection of it to the moduli space $R_g$ of genus $g$ Prym curves\, that is\
, of pairs $(C\,\\eta)$\, where $\\eta$ is a nontrivial $2$-torsion elemen
t in $Pic(C)$. I will give an overview of recent results on this map obtai
ned in a work in progress with Margherita Lelli-Chiesa\nand Alessandro Ver
ra and how degenerations of Nikulin surfaces to surfaces that are biration
al to unions of rational ruled surfaces are of help.\n\nhttps://indico.mat
h.cnrs.fr/event/1242/contributions/50/
LOCATION:Poitiers 0-6
URL:https://indico.math.cnrs.fr/event/1242/contributions/50/
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BEGIN:VEVENT
SUMMARY:Isogenies and transcendental Hodge structures of K3 surfaces
DTSTART;VALUE=DATE-TIME:20161124T151500Z
DTEND;VALUE=DATE-TIME:20161124T160500Z
DTSTAMP;VALUE=DATE-TIME:20191118T160603Z
UID:indico-contribution-1242-49@indico.math.cnrs.fr
DESCRIPTION:Speakers: Samuel Boissière ()\nEvery Hodge class on a product
of two complex projective K3 surfaces induces a homomorphism of rational
Hodge structures between the respective transcendental lattices. Under the
hypothesis that this morphism is an isometry of rational quadratic spaces
\, Mukai\, Nikulin and recently Buskin have proven that the corresponding
Hodge class is algebraic\, confirming the Hodge conjecture in this context
. In this talk\, I will show that the hypothesis of isometry is too restri
ctive by constructing geometrically some families of isogenies between K3
surfaces whose transcendental Hodge structures are nonisometric. This is a
collaboration with Alessandra Sarti and Davide Cesera Veniani.\n\nhttps:/
/indico.math.cnrs.fr/event/1242/contributions/49/
LOCATION:Poitiers 0-6
URL:https://indico.math.cnrs.fr/event/1242/contributions/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Explicit Schoen surfaces
DTSTART;VALUE=DATE-TIME:20161125T081000Z
DTEND;VALUE=DATE-TIME:20161125T090000Z
DTSTAMP;VALUE=DATE-TIME:20191118T160603Z
UID:indico-contribution-1242-48@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alessandra Sarti ()\nI will present an explicit geom
etric construction\nof some special surfaces of general type described\nby
Schoen in 2007\, that occupy an important place in the geography\nof surf
aces of general type. I will show how the construction\ninvolves the Segre
cubic\, the Igusa quartic\nand K3 quartic surfaces with fifteen nodes.\nT
his is a joint work with Carlos Rito and Xavier Roulleau.\n\nhttps://indic
o.math.cnrs.fr/event/1242/contributions/48/
LOCATION:Poitiers 0-6
URL:https://indico.math.cnrs.fr/event/1242/contributions/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abelian varieties and Minkowski-Hlawka theorem
DTSTART;VALUE=DATE-TIME:20161125T092000Z
DTEND;VALUE=DATE-TIME:20161125T101000Z
DTSTAMP;VALUE=DATE-TIME:20191118T160603Z
UID:indico-contribution-1242-47@indico.math.cnrs.fr
DESCRIPTION:Speakers: Pascal Autissier ()\nA classical theorem of Minkowsk
i and Hlawka states that\nthere exists a lattice in $R^n$ with packing den
sity at least $2^{1-n}$. Buser and\nSarnak proved the analogue of this res
ult in the context of complex abelian\nvarieties. Here we give an improvem
ent of this analogue\; this shows a\nconjecture of Muetzel.\n\nhttps://ind
ico.math.cnrs.fr/event/1242/contributions/47/
LOCATION:Poitiers 0-6
URL:https://indico.math.cnrs.fr/event/1242/contributions/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Around the geometry of Calogero-Moser spaces
DTSTART;VALUE=DATE-TIME:20161124T130000Z
DTEND;VALUE=DATE-TIME:20161124T135000Z
DTSTAMP;VALUE=DATE-TIME:20191118T160603Z
UID:indico-contribution-1242-46@indico.math.cnrs.fr
DESCRIPTION:Speakers: Cédric Bonnafé ()\nNumerical evidences suggest tha
t the representation theory\nof a finite reductive group should be connect
ed to the geometry of\nthe Calogero-Moser variety associated with its corr
esponding Weyl group.\nDespite we have no (serious) clue for what should b
e the link\, pursuing\nthis analogy leads to new questions about the geome
try of this variety\,\nwhich might have an interest by themselves: symplec
tic resolutions\,\nPoisson structure and symplectic leaves\, fixed points\
, equivariant\ncohomology.\n\nhttps://indico.math.cnrs.fr/event/1242/contr
ibutions/46/
LOCATION:Poitiers 0-6
URL:https://indico.math.cnrs.fr/event/1242/contributions/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:GIT vs Baily-Borel compactification for the moduli space of Quarti
c Surfaces
DTSTART;VALUE=DATE-TIME:20161124T140500Z
DTEND;VALUE=DATE-TIME:20161124T145500Z
DTSTAMP;VALUE=DATE-TIME:20191118T160603Z
UID:indico-contribution-1242-45@indico.math.cnrs.fr
DESCRIPTION:Speakers: Radu Laza ()\nThis is a report on joint work with Ki
eran O'Grady. The period map from the GIT moduli space of quartic surfaces
to the Baily-Borel compactification of the period space is birational but
far from regular. New birational models of locally symmetric varieties of
Type IV have been introduced by Looijenga\, in order to study similar pro
blems. Looijenga's construction does not succeed in “explaining” the p
eriod map for quartic surfaces. We discovered that one can (conjecturally)
reconcile Looijenga's philosophy with the phenomenology of quartic surfac
es\, provided one takes into account suitable Borcherd relations between d
ivisor classes on relevant locally symmetric varieties. We work with a tow
er of locally symmetric varieties\, in particular our results should also
“explain” the period map for double EPW sextics.\n\nhttps://indico.mat
h.cnrs.fr/event/1242/contributions/45/
LOCATION:Poitiers 0-6
URL:https://indico.math.cnrs.fr/event/1242/contributions/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volume of complex hyperbolic structures on moduli spaces of genus
zero curves
DTSTART;VALUE=DATE-TIME:20161124T104500Z
DTEND;VALUE=DATE-TIME:20161124T113500Z
DTSTAMP;VALUE=DATE-TIME:20191118T160603Z
UID:indico-contribution-1242-44@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vincent Koziarz ()\n(joint work with D. M. Nguyen):\
nI will show that the complex hyperbolic metrics defined by Deligne-Mostow
and Thurston on the moduli space of genus $0$ curves with $n$ marked poin
ts $M_{0\,n}$ are singular Kaehler-Einstein metrics when $M_{0\,n}$ is emb
edded in its Deligne-Mumford-Knudsen compactification. As a consequence\,
I will obtain a formula computing the volume of $M_{0\,n}$ with respect to
these metrics using intersection of boundary divisors of its compactifica
tion.\nIn the case when the weights parametrizing the complex hyperbolic s
tructures are rational\, following an idea of Y. Kawamata\, I will show th
at the associated metrics actually represent the first Chern class of some
line bundles on the compactification of $M_{0\,n}$\, from which other for
mulas computing the same volumes will be derived.\n\nhttps://indico.math.c
nrs.fr/event/1242/contributions/44/
LOCATION:Poitiers 0-6
URL:https://indico.math.cnrs.fr/event/1242/contributions/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hypersurfaces in projective schemes and Bertini's theorem
DTSTART;VALUE=DATE-TIME:20161124T083000Z
DTEND;VALUE=DATE-TIME:20161124T092000Z
DTSTAMP;VALUE=DATE-TIME:20191118T160603Z
UID:indico-contribution-1242-43@indico.math.cnrs.fr
DESCRIPTION:Speakers: Qing Liu ()\nLet $X$ be a projective scheme over an
affine base. We develop a technique for proving the existence of closed su
bschemes $H$ with various favorable properties. We offer several applicati
ons of this technique\, including the existence of hypersurfaces in $X$ co
ntaining a given closed subscheme and intersecting properly a given closed
set\, and the existence of finite quasi-sections. This is joint work with
O. Gabber and D. Lorenzini.\n\nhttps://indico.math.cnrs.fr/event/1242/con
tributions/43/
LOCATION:Poitiers 0-6
URL:https://indico.math.cnrs.fr/event/1242/contributions/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nodal hypersurfaces with defect\, Alexander polynomials and Mordel
l-Weil groups
DTSTART;VALUE=DATE-TIME:20161124T094000Z
DTEND;VALUE=DATE-TIME:20161124T103000Z
DTSTAMP;VALUE=DATE-TIME:20191118T160603Z
UID:indico-contribution-1242-42@indico.math.cnrs.fr
DESCRIPTION:Speakers: Remke Kloosterman ()\nIn this talk we present a shor
t proof for Cheltsov's result that a nodal hypersurface of degree $d$ in $
P^4$ which is not factorial\, has at least $(d-1)^2$ nodes. We will discus
s how variants of these arguments yields interesting results on the fundam
ental group of the complement of a singular plane curve and on the Mordell
-Weil group of certain abelian varieties over function fields of character
istic zero.\n\nhttps://indico.math.cnrs.fr/event/1242/contributions/42/
LOCATION:Poitiers 0-6
URL:https://indico.math.cnrs.fr/event/1242/contributions/42/
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