Pinar Kilicer

Pinar Kilicer
University of Groningen | RUG · Johann Bernoulli Institute for Mathematics and Computer Science (JBI)

Doctor of Philosophy

About

9
Publications
712
Reads
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57
Citations
Additional affiliations
September 2018 - present
University of Groningen
Position
  • PostDoc Position
July 2016 - September 2018
Carl von Ossietzky Universität Oldenburg
Position
  • PostDoc Position
April 2016 - July 2016
Max Planck Institute for Mathematics
Position
  • PostDoc Position
Education
September 2012 - July 2016
Leiden University
Field of study
  • Mathematics
September 2009 - September 2011
Koc University
Field of study
  • Mathematics
September 2004 - July 2009
Middle East Technical University
Field of study
  • Mathematics

Publications

Publications (9)
Preprint
Full-text available
We study a 3-dimensional stratum $\mathcal{M}_{3,V}$ of the moduli space $\mathcal{M}_3$ of curves of genus $3$ parameterizing curves $Y$ that admit a certain action of $V\simeq C_2\times C_2$. We determine the possible types of the stable reduction of these curves to characteristic different from $2$. We define invariants for $\mathcal{M}_{3,V}$ a...
Article
Full-text available
In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler, and Zykin, which allows us to connect invariants of binary octics to Siegel modular forms of genus 3. We use this connection to show that certain modular functions, when restricted to the hyperelliptic locus, assume values whose denominators are products of powers of primes...
Preprint
In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler, and Zykin, which allows us to connect invariants of binary oc-tics to Siegel modular forms of genus 3. We use this connection to show that certain modular functions, when restricted to the hyperelliptic locus, assume values whose denominators are products of powers of prime...
Article
Full-text available
We give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Our proof is simpler than the previous proofs for genus 2 and 3 and, unlike previous bounds for genus 3, our bounds are sharp enough for use in class polynomial computation.
Article
Full-text available
We give examples of smooth plane quartics over $Q$ with complex multiplication over $\overline{Q}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of period matrices, the fast computation of Dixmier-Ohno invariants, and reconstruction from these invariants. Finally, we discuss som...
Article
Full-text available
We give bounds on the primes of geometric bad reduction for curves of genus 3 3 of primitive complex multiplication (CM) type in terms of the CM orders. In the case of elliptic curves, there are no primes of geometric bad reduction because CM elliptic curves are CM abelian varieties, which have potential good reduction everywhere. However, for genu...
Thesis
Let E be an elliptic curve over C with complex multiplication (CM) by the maximal order OK of an imaginary quadratic field K. The first main theorem of complex multiplication for elliptic curves then states that the field extension K(j(E)), obtained by adjoining the j-invariant of E to K, is equal to the Hilbert class field of K, see Theorem 11.1 i...
Article
Full-text available
The CM class number one problem for elliptic curves asked to find all elliptic curves defined over the rationals with non-trivial endomorphism ring. For genus-2 curves it is the problem of determining all CM curves of genus $2$ defined over the reflex field. We solve the problem by showing that the list given in Bouyer and Streng [LMS J. Comput. Ma...

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