Oh boy, this question. I did a quick r/AskHistorians search to see if it had been answered before (as I was sure it must have been), but came up empty handed. It's really an honor (though a dubious one) to be able to contribute to the AH record on this topic. I really hope my answer lives up to the gravity this question demands and deserves.

Before we launch into a discussion about whether or not Joseph Stalin intentionally sought to starve out his opponents in an attempt to crush Ukrainian nationalism during the famine in Ukraine of 1932-1933, which has come to be remembered as Голодомор (Holodomor, meaning roughly Mass Death by Starvation), I think the best course of action with which to start is just to enumerate some of the undisputed facts concerning this unmitigated tragedy so that anyone who might be tempted into entertaining some kind of denialism or speculation around this topic be forced to immediately account for them. [1] It frees up any further dialogue from having to restate the central issues as well.

• Up to 5 million men, women, and children were starved to death between 1932 and 1935 in Ukraine, that means (if we accept the barest minimum plausible figure of 3 million deaths) that for those three years no fewer than 30,000 human beings died every single day, on average. [2]
• These deaths were the direct result of Soviet policy which dictated that any and all grain be confiscated, ration distribution be ceased, and free movement (i.e. fleeing this man-made hell on earth) be restricted. [3]
• During and after the famine, the Soviet state actively spread denialism and disinformation concerning the events and Soviet secret police and intelligence agencies forced entry into various local government archival offices where deaths were registered and destroyed immediately or confiscated and then destroyed nearly all extant records of these deaths. [4]

I don't say all that to try to trigger an emotional reaction in the reader before I slide in some ill-informed editorializing about what Stalin was up to, but like I said at the outset, when discussing things like the Holodomor it is absolutely critical that we not lose sight of what is and what is not up for debate here (even by those who might not agree with anyone else's conclusions).

I also want to step back and define the term genocide so there can be no confusion about what the underlying question in the OP is asking about. The Convention on the Prevention and Punishment of the Crime of Genocide (1948) from the United Nations offers a succinct definition we can use:

In the present Convention, genocide means any of the following acts committed with intent to destroy, in whole or in part, a national, ethnical, racial or religious group:

(a) Killing members of the group;

(b) Causing serious bodily or mental harm to members of the group;

(c) Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part;

(d) Imposing measures intended to prevent births within the group;

(e) Forcibly transferring children of the group to another group. [5]

So I hope by this point that there is no doubt in anyone's mind that the people of Ukraine (whether or not they were ethnically Ukrainians) were killed. They were harmed bodily and mentally. Their life conditions were inflicted upon so as to bring about physical destruction. Measures were imposed upon them that prevented births. Their children were transferred to another group, i.e. the no longer alive. We just went right down the list and, there is no debate about whether or not these things happened. The only question that is at all ambiguous is whether or not this was done on a racially motivated basis.

The source above Population Losses in the Holodomor and the Destruction of Related Archives: New Archival Evidence indicates that we have existing records for approximately 650,000 deaths during this period in Ukraine. That is the primary reason why there is such disparity in the estimations of various parties concerning the actual number of deaths which took place. Again though, this isn't a debate about the substantive results of this famine-- it's about the intentions.

I may remember incorrectly, but i had access to some primary souces as a university student during the glasnost era. I was preparing for a PhD on vygotsky at the time but was also randimly searching details of my family. As i remember the record stated that Stalin's entourage were on a train with his wife Nedezhda as it went through the Ukraine. It was an armoured train with steel window shields which were raised for a moment to reveal hundreds of starving women and children begging for grain. They were forcibly restrained from knocking on the train sides by soldiers. Shortly after stalin's wife shot herself over an argument about collectivisation. I have tried to find the documentary evidence online since (i changed my line of post graduate study from history to computer science). These records, and those of the Kazakhstan famine, seem no longer to be around or at least, easily available. The reason i was interested was bc my family were in both locations post famine and often talked about it. I wanted to confirm/deny their oral first hand accounts. Apparently during a dinner sometime after, Stalin's wife wanted grain to be distributed to the women and children, and he insisted that only non saboteurs were permitted to eat. She said that the children were innocent and shot herself. The odd thing is that access to these files seems no longer to be available, but they were very detailed. The secret police and administration kept a lot of detailed records. For example, i found my mother's name quite easily at the time. I don't think such access is available any longer. Note: I'm not sure if this counts as a proper source and am happy to be removed.

There's been some very good answers by /u/Kochevnik81 and /u/amp1212 touching on this question.