19 dec 2019
Trieste
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YOUNG ALGEBRAIC GEOMETRY MEETING
TRIESTE, DECEMBER 19, 2019
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VENUE: room 5B and room Aula Morin 2A Dipartimento di Matematica e Geoscienze via Valerio 12/1 Trieste
PROGRAM
- 10:00 - 11:00 MARTA PANIZZUT (Institut für Mathematik TU Berlin)
TROPICAL CUBIC SURFACES
room 5B - fifth floor
- 11:30 - 12:30 DE-QI ZHANG (National University of Singapore)
EQUIVARIANT MINIMAL MODEL PROGRAM WITH A VIEW
TOWARDS ALGEBRAIC AND ARITHMETIC DYNAMICS
room 5B - fifth floor
Abstract: We will elaborate the notion of ‘int-amplified’ endomorphism f of a normal projective variety X, a property weaker than ‘polarized’ yet preserved by products. We will show that the existence of such a single f guarantees that every Minimal Model Program (MMP) is equivariant w.r.t. a finite-index submonoid of the whole monoid SEnd(X) of all surjective endomorphisms of X. Applications of the equivariant MMP are discussed: Kawaguchi-Silverman conjecture on the equivalence of arithmetic and dynamic degrees of an endomorphism, and characterization of a subvariety with Zariski dense periodic points. Some parts are based on joint work with Meng.
- 14:00 - 15:00 GIORGIO SCATTAREGGIA (University of Bergen - Norway)
DEFORMATION THEORY OF MAXIMAL IDEAL POLARIZATIONS.
room Aula Morin - second floor
Abstract. In the analysis of monomial ideals, the operation called “polarization” is used to reduce monomial ideals to square-free monomial ideals. The advantage of dealing with square-free monomial ideals is that one can use the Stanley-Reisner correspondence, which provides a correlation between square-free monomial ideals and simplicial complexes. Let k be a field, and let S = kx_1, … , x_n be the polynomial ring in n variables over k. We are interested in studying the polarizations of the d-powers of the maximal ideal m =(x1, … , xn). In 2013 H. Lohne made a thorough investigation of the deformation properties of the two special cases, namely the standard polarization and the box polarization. However, not much is known for all the other possibilities. In this seminar we recall the definition of polarization of a monomial ideal and we show some examples of such polarizations. Then we discuss the case of the standard polarization and the box polarization. Finally we discuss the example of a particularly “weird” polarization and we use a computer-algebra software to get some insights of its behaviour.
- 15:00 - 16:00 LUCA SODOMACO (Aalto University, Department of
Mathematics and Systems Analysis, Espoo, Finland)
ON THE EUCLIDEAN DISTANCE POLYNOMIAL OF A REAL
ALGEBRAIC VARIETY
room Aula Morin - second floor
- 16:15- 17:15 FABIO TANTURRI (Dipartimento di Matematica "Giuseppe
Peano" - Torino)
ON ABELIAN SURFACES, COBLE HYPERSURFACES, AND
ORBITAL DEGENERACY LOCI
room Aula Morin - second floor
Organizers: V. Beorchia, E. Mezzetti, F. Perroni
EVERYBODY INTERESTED IS MUCH WELCOME TO ATTEND