**Sławomir Rams**

Associate Professor

# Research interests

My main scientific interests lie in problems closely related to the geometry of projective surfaces and threefolds. Although I profoundly admire sophistication of abstract language and I like to use modern tools of algebraic geometry, I find many down-to-earth classical open problems of algebraic geometry very interesting (and challenging).

My approach may result from the fact that after completing my Ph.D. thesis on local theory at the Jagiellonian University (Ph.D. thesis awarded the Prize of the Prime Minister of the Republic of Poland), I moved to Erlangen (the chair of Prof. W.P. Barth), where I had the chance to see the beauty of classical geometry. I got my habilitation in Erlangen in 2006 and came back to Poland to carry out my research as an associate professor at the Institute of Mathematics of the Jagiellonian University.

## Lines on surfaces

Various questions related to the configurations of lines on (hyper)surfaces in P_{3}(C).

#### Papers

- S. Rams, M. Schuett,
*On quartics with lines of the second kind*, (pdf file)

submitted - S. Rams, M. Schuett,
*64 lines on smooth quartic surfaces*, (pdf file)

submitted - S. Rams,
*Projective surfaces with many skew lines.*(paper page)

Proc. Am. Math. Soc. 133 (2005), No.1, 11-13. - S. Rams,
*Three-divisible families of skew lines on a smooth projective quintic.*(paper page)

Trans. Am. Math. Soc. 354 (2002), 2359-2367.

## Surfaces

Surfaces with A-D-E singularities and their resolutions, divisible sets of singularities, K3 surfaces. Quintics.

#### Papers

- S. Rams, M. Schuett,
*The Barth quintic surface has Picard number 41.*(pdf file)

Ann. Scuola Norm. Sup. Pisa Cl. Sci., to appear. - S. Cynk, S. Rams,
*On a map between two K3 surfaces associated to a net of quadrics.*(paper page)

Arch. Math. (Basel) 88 (2007), no. 2, 109–122. - W. P. Barth, S. Rams,
*Cusps and Codes.*(pdf file)

Math. Nachr. 280 (2007), no. 1-2, 50–59. - W. P. Barth, S. Rams,
*Equations of low-degree projective surfaces with three-divisible sets of cusps.*(pdf file)

Math. Zeit. 249 (2005), 283-295.

## Local theory

Generalizations of the notion of intersection multiplicity in (local) analytic case. Extended index of intersection. Segre numbers.

#### Papers

- S. Rams,
*On the index of contact and multiplicities for bigraded rings*, (paper page)

Manuscr. Math. 106 (2001), 339-347. - R. Achilles, S. Rams,
*Intersection numbers, Segre numbers and generalized Samuel multiplicities.*(paper page)

Arch. Math. (Basel) 77 (2001), 391-398. - S. Rams,
*On intersection product of analytic cycles*, (pdf file)

Ann. Polon. Math. 73, 135-146 (2000)

## Threefolds

Formulae for Hodge numbers of threefolds. Notion of the defect of a singular threefold. Calabi-Yau threefolds. Factoriality. Calabi-Yau threefolds.

#### Papers

- S. Cynk, S. Rams,
*Non-factorial nodal complete intersection threefolds.*(pdf file)

Communications in Contemporary Mathematics, to appear. - S. Cynk, S. Rams,
*On Calabi-Yau threefolds associated to a web of quadrics.*(pdf file)

Forum Math., to appear. - S. Cynk, S. Rams,
*Defect via differential forms with logarithmic poles*, (pdf file)

Math. Nachr. 284 (2011), no. 17-18, 2148–2158. - S. Rams,
*Defect and Hodge numbers of hypersurfaces.*(pdf file)

Adv. Geom. 8 (2008), no. 2, 257–288.